Yang Leng
Materials Characterization
Werner, W.S. (ed.)
Zolotoyabko, E.
Characterization of Surfaces
and Nanostructures
Basic Concepts of X-Ray
Diffraction
Academic and Industrial Applications
2008
2014
ISBN: 978-3-527-33561-9
ISBN: 978-3-527-31760-8
Abou-Ras, D., Kirchartz, T., Rau, U. (eds.)
Che, M., Vedrine, J.C. (eds.)
Characterization of Solid
Materials and Heterogeneous
Catalysts
From Structure to Surface Reactivity
2012
ISBN: 978-3-527-32687-7
Mittal, V. (ed.)
Characterization Techniques for
Polymer Nanocomposites
2012
ISBN: 978-3-527-33148-2
Advanced Characterization
Techniques for Thin Film Solar
Cells
2011
ISBN: 978-3-527-41003-3
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Related Titles
Materials Characterization
Introduction to Microscopic and Spectroscopic Methods
Second Edition
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Yang Leng
Prof. Yang Leng
The Hong Kong University of Science &
Technology
Department of Mechanical Engineering
Clear Water Bay
Kowloon
Hong Kong
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The Author
To Ashley and Lewis
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V
Contents
1
1.1
1.1.1
1.1.2
1.1.2.1
1.1.2.2
1.1.3
1.1.4
1.2
1.2.1
1.2.2
1.2.2.1
1.2.2.2
1.3
1.3.1
1.3.1.1
1.3.1.2
1.3.2
1.3.3
1.3.3.1
1.3.3.2
1.3.4
1.4
1.4.1
1.4.2
1.4.3
1.4.4
1.4.5
1.5
1.5.1
1.5.2
Light Microscopy 1
Optical Principles 1
Image Formation 1
Resolution 3
Effective Magnification 5
Brightness and Contrast 5
Depth of Field 6
Aberrations 7
Instrumentation 9
Illumination System 9
Objective Lens and Eyepiece 13
Steps for Optimum Resolution 15
Steps to Improve Depth of Field 15
Specimen Preparation 15
Sectioning 16
Cutting 16
Microtomy 17
Mounting 17
Grinding and Polishing 19
Grinding 19
Polishing 21
Etching 23
Imaging Modes 26
Bright-Field and Dark-Field Imaging 26
Phase-Contrast Microscopy 27
Polarized-Light Microscopy 30
Nomarski Microscopy 35
Fluorescence Microscopy 37
Confocal Microscopy 39
Working Principles 39
Three-Dimensional Images 41
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VII
Contents
References 45
Further Reading 45
2
2.1
2.1.1
2.1.2
2.2
2.2.1
2.2.1.1
2.2.1.2
2.2.1.3
2.2.2
2.2.2.1
2.3
2.3.1
2.3.1.1
2.3.2
2.3.2.1
2.3.2.2
2.3.3
2.3.3.1
2.3.3.2
2.3.3.3
2.3.4
2.3.4.1
2.3.4.2
2.4
2.4.1
2.4.2
X-Ray Diffraction Methods 47
X-Ray Radiation 47
Generation of X-Rays 47
X-Ray Absorption 50
Theoretical Background of Diffraction 52
Diffraction Geometry 52
Bragg’s Law 52
Reciprocal Lattice 53
Ewald Sphere 55
Diffraction Intensity 58
Structure Extinction 60
X-Ray Diffractometry 62
Instrumentation 62
System Aberrations 64
Samples and Data Acquisition 65
Sample Preparation 65
Acquisition and Treatment of Diffraction Data 65
Distortions of Diffraction Spectra 67
Preferential Orientation 67
Crystallite Size 68
Residual Stress 69
Applications 70
Crystal-Phase Identification 70
Quantitative Measurement 72
Wide-Angle X-Ray Diffraction and Scattering 75
Wide-Angle Diffraction 76
Wide-Angle Scattering 79
References 82
Further Reading 82
3
3.1
3.1.1
3.1.1.1
3.1.1.2
3.1.2
3.1.3
3.2
3.2.1
3.2.2
3.2.2.1
3.2.2.2
Transmission Electron Microscopy 83
Instrumentation 83
Electron Sources 84
Thermionic Emission Gun 85
Field Emission Gun 86
Electromagnetic Lenses 87
Specimen Stage 89
Specimen Preparation 90
Prethinning 91
Final Thinning 91
Electrolytic Thinning 91
Ion Milling 92
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VIII
3.2.2.3
3.3
3.3.1
3.3.2
3.3.3
3.3.3.1
3.3.3.2
3.4
3.4.1
3.4.2
3.4.2.1
3.4.2.2
3.4.3
3.4.4
3.5
3.5.1
3.5.2
3.5.3
Ultramicrotomy 93
Image Modes 94
Mass–Density Contrast 95
Diffraction Contrast 96
Phase Contrast 101
Theoretical Aspects 102
Two-Beam and Multiple-Beam Imaging 105
Selected-Area Diffraction (SAD) 107
Selected-Area Diffraction Characteristics 107
Single-Crystal Diffraction 109
Indexing a Cubic Crystal Pattern 109
Identification of Crystal Phases 112
Multicrystal Diffraction 114
Kikuchi Lines 114
Images of Crystal Defects 117
Wedge Fringe 117
Bending Contours 120
Dislocations 122
References 126
Further Reading 126
4
4.1
4.1.1
4.1.2
4.1.2.1
4.1.3
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.1.1
4.4.2
4.4.3
4.5
4.5.1
4.5.2
4.5.3
4.6
Scanning Electron Microscopy 127
Instrumentation 127
Optical Arrangement 127
Signal Detection 129
Detector 130
Probe Size and Current 131
Contrast Formation 135
Electron–Specimen Interactions 135
Topographic Contrast 137
Compositional Contrast 139
Operational Variables 141
Working Distance and Aperture Size 141
Acceleration Voltage and Probe Current 144
Astigmatism 145
Specimen Preparation 145
Preparation for Topographic Examination 146
Charging and Its Prevention 147
Preparation for Microcomposition Examination 149
Dehydration 149
Electron Backscatter Diffraction 151
EBSD Pattern Formation 151
EBSD Indexing and Its Automation 153
Applications of EBSD 155
Environmental SEM 156
IX
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Contents
Contents
4.6.1
4.6.2
ESEM Working Principle
Applications 158
References 160
Further Reading 160
156
5
5.1
5.1.1
5.1.2
5.2
5.2.1
5.2.2
5.2.3
5.2.4
5.3
5.3.1
5.3.1.1
5.3.1.2
5.3.1.3
5.3.1.4
5.3.2
5.3.3
5.3.3.1
5.3.3.2
5.3.3.3
5.3.4
5.3.4.1
5.3.4.2
5.3.4.3
5.3.4.4
5.4
5.4.1
5.4.2
5.4.3
Scanning Probe Microscopy 163
Instrumentation 163
Probe and Scanner 165
Control and Vibration Isolation 165
Scanning Tunneling Microscopy 166
Tunneling Current 166
Probe Tips and Working Environments
Operational Modes 168
Typical Applications 169
Atomic Force Microscopy 170
Near-Field Forces 170
Short-Range Forces 171
van der Waals Forces 171
Electrostatic Forces 171
Capillary Forces 172
Force Sensors 172
Operational Modes 174
Static Contact Modes 176
Lateral Force Microscopy 177
Dynamic Operational Modes 177
Typical Applications 180
Static Mode 180
Dynamic Noncontact Mode 181
Tapping Mode 182
Force Modulation 183
Image Artifacts 183
Tip 183
Scanner 185
Vibration and Operation 187
References 189
Further Reading 189
6
6.1
6.1.1
6.1.1.1
6.1.2
6.2
6.2.1
6.2.1.1
X-Ray Spectroscopy for Elemental Analysis 191
Features of Characteristic X-Rays 191
Types of Characteristic X-Rays 193
Selection Rules 193
Comparison of K, L, and M Series 194
X-Ray Fluorescence Spectrometry 196
Wavelength Dispersive Spectroscopy 199
Analyzing Crystal 200
167
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X
6.2.1.2
6.2.2
6.2.2.1
6.2.2.2
6.2.2.3
6.2.3
6.3
6.3.1
6.3.2
6.4
6.4.1
6.4.2
6.4.2.1
6.4.2.2
6.4.2.3
Wavelength Dispersive Spectra 201
Energy Dispersive Spectroscopy 203
Detector 203
Energy Dispersive Spectra 204
Advances in Energy Dispersive Spectroscopy 204
XRF Working Atmosphere and Sample Preparation 206
Energy Dispersive Spectroscopy in Electron Microscopes 207
Special Features 208
Scanning Modes 210
Qualitative and Quantitative Analysis 211
Qualitative Analysis 211
Quantitative Analysis 213
Quantitative Analysis by X-Ray Fluorescence 214
Fundamental Parameter Method 215
Quantitative Analysis in Electron Microscopy 216
References 219
Further Reading 219
7
7.1
7.1.1
7.1.2
7.2
7.2.1
7.2.2
7.2.2.1
7.2.2.2
7.2.2.3
7.2.3
7.3
7.3.1
7.3.2
7.4
7.4.1
7.4.1.1
7.4.1.2
7.4.1.3
7.4.2
7.4.2.1
7.4.3
Electron Spectroscopy for Surface Analysis 221
Basic Principles 221
X-Ray Photoelectron Spectroscopy 221
Auger Electron Spectroscopy 222
Instrumentation 225
Ultrahigh Vacuum System 225
Source Guns 227
X-Ray Gun 227
Electron Gun 228
Ion Gun 229
Electron Energy Analyzers 229
Characteristics of Electron Spectra 230
Photoelectron Spectra 230
Auger Electron Spectra 233
Qualitative and Quantitative Analysis 235
Qualitative Analysis 235
Peak Identification 239
Chemical Shifts 239
Problems with Insulating Materials 241
Quantitative Analysis 246
Peaks and Sensitivity Factors 246
Composition Depth Profiling 247
References 250
Further Reading 251
XI
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Contents
Contents
8
8.1
8.1.1
8.1.2
8.2
8.2.1
8.2.1.1
8.2.1.2
8.2.2
8.2.2.1
8.2.2.2
8.2.2.3
8.3
8.3.1
8.3.1.1
8.3.1.2
8.3.1.3
8.3.2
8.3.2.1
8.4
8.4.1
8.4.2
8.5
8.5.1
8.5.2
8.5.2.1
8.5.2.2
8.5.2.3
Secondary Ion Mass Spectrometry for Surface Analysis
Basic Principles 253
Secondary Ion Generation 254
Dynamic and Static SIMS 257
Instrumentation 258
Primary Ion System 258
Ion Sources 259
Wien Filter 262
Mass Analysis System 262
Magnetic Sector Analyzer 263
Quadrupole Mass Analyzer 264
Time-of-Flight Analyzer 264
Surface Structure Analysis 266
Experimental Aspects 266
Primary Ions 266
Flood Gun 266
Sample Handling 267
Spectrum Interpretation 268
Element Identification 269
SIMS Imaging 272
Generation of SIMS Images 274
Image Quality 275
SIMS Depth Profiling 275
Generation of Depth Profiles 276
Optimization of Depth Profiling 276
Primary Beam Energy 278
Incident Angle of Primary Beam 278
Analysis Area 279
References 282
9
9.1
9.1.1
9.1.2
9.1.3
9.1.3.1
9.1.3.2
9.1.4
9.1.4.1
9.1.4.2
9.1.5
9.1.5.1
9.1.5.2
9.2
9.2.1
Vibrational Spectroscopy for Molecular Analysis 283
Theoretical Background 283
Electromagnetic Radiation 283
Origin of Molecular Vibrations 285
Principles of Vibrational Spectroscopy 286
Infrared Absorption 286
Raman Scattering 287
Normal Mode of Molecular Vibrations 289
Number of Normal Vibration Modes 291
Classification of Normal Vibration Modes 291
Infrared and Raman Activity 292
Infrared Activity 293
Raman Activity 295
Fourier Transform Infrared Spectroscopy 297
Working Principles 298
253
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XII
9.2.2
9.2.2.1
9.2.2.2
9.2.2.3
9.2.2.4
9.2.3
9.2.3.1
9.2.3.2
9.2.3.3
9.2.3.4
9.2.4
9.2.4.1
9.2.4.2
9.3
9.3.1
9.3.1.1
9.3.1.2
9.3.1.3
9.3.1.4
9.3.1.5
9.3.2
9.3.3
9.3.4
9.3.4.1
9.3.4.2
9.3.4.3
9.3.4.4
9.3.4.5
9.4
9.4.1
9.4.1.1
9.4.1.2
9.4.1.3
9.4.2
9.4.2.1
9.4.2.2
Instrumentation 300
Infrared Light Source 300
Beamsplitter 300
Infrared Detector 301
Fourier Transform Infrared Spectra 302
Examination Techniques 304
Transmittance 304
Solid Sample Preparation 304
Liquid and Gas Sample Preparation 304
Reflectance 305
Fourier Transform Infrared Microspectroscopy 307
Instrumentation 307
Applications 309
Raman Microscopy 310
Instrumentation 310
Laser Source 311
Microscope System 311
Prefilters 312
Diffraction Grating 313
Detector 314
Fluorescence Problem 314
Raman Imaging 315
Applications 316
Phase Identification 317
Polymer Identification 319
Composition Determination 319
Determination of Residual Strain 321
Determination of Crystallographic Orientation 322
Interpretation of Vibrational Spectra 323
Qualitative Methods 323
Spectrum Comparison 323
Identifying Characteristic Bands 324
Band Intensities 327
Quantitative Methods 327
Quantitative Analysis of Infrared Spectra 327
Quantitative Analysis of Raman Spectra 330
References 331
Further Reading 332
10
10.1
10.1.1
10.1.1.1
10.1.2
10.1.3
Thermal Analysis 333
Common Characteristics 333
Thermal Events 333
Enthalpy Change 335
Instrumentation 335
Experimental Parameters 336
XIII
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Contents
Contents
10.2
10.2.1
10.2.1.1
10.2.1.2
10.2.1.3
10.2.2
10.2.2.1
10.2.2.2
10.2.2.3
10.2.3
10.2.3.1
10.2.3.2
10.2.3.3
10.2.4
10.2.4.1
10.2.4.2
10.2.4.3
10.3
10.3.1
10.3.2
10.3.2.1
10.3.2.2
10.3.2.3
10.3.2.4
10.3.3
10.3.3.1
10.3.3.2
10.3.4
Differential Thermal Analysis and Differential Scanning
Calorimetry 337
Working Principles 337
Differential Thermal Analysis 337
Differential Scanning Calorimetry 338
Temperature-Modulated Differential Scanning Calorimetry 340
Experimental Aspects 342
Sample Requirements 342
Baseline Determination 343
Effects of Scanning Rate 344
Measurement of Temperature and Enthalpy Change 345
Transition Temperatures 345
Measurement of Enthalpy Change 347
Calibration of Temperature and Enthalpy Change 348
Applications 348
Determination of Heat Capacity 348
Determination of Phase Transformation and Phase Diagrams 350
Applications to Polymers 351
Thermogravimetry 353
Instrumentation 354
Experimental Aspects 355
Samples 355
Atmosphere 356
Temperature Calibration 358
Heating Rate 359
Interpretation of Thermogravimetric Curves 360
Types of Curves 360
Temperature Determination 362
Applications 362
References 365
Further Reading 365
Index
367
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XIV
1
Light Microscopy
Light or optical microscopy is the primary means for scientists and engineers
to examine the microstructure of materials. The history of using a light microscope for microstructural examination of materials can be traced back to the
1880s. Since then, light microscopy has been widely used by metallurgists to
examine metallic materials. Light microscopy for metallurgists became a special
field named metallography. The basic techniques developed in metallography are
not only used for examining metals, but also are used for examining ceramics
and polymers. In this chapter, light microscopy is introduced as a basic tool
for microstructural examination of materials including metals, ceramics, and
polymers.
1.1
Optical Principles
1.1.1
Image Formation
Reviewing the optical principles of microscopes should be the first step to understanding light microscopy. The optical principles of microscopes include image
formation, magnification, and resolution. Image formation can be illustrated by the
behavior of a light path in a compound light microscope as shown in Figure 1.1.
A specimen (object) is placed at position A where it is between one and two focal
lengths from an objective lens. Light rays from the object first converge at the
objective lens and are then focused at position B to form a magnified inverted
image. The light rays from the image are further converged by the second lens
(projector lens) to form a final magnified image of an object at C.
The light path shown in Figure 1.1 generates the real image at C on a screen
or camera film, which is not what we see with our eyes. Only a real image can be
formed on a screen and photographed. When we examine microstructure with our
eyes, the light path in a microscope goes through an eyepiece instead of projector lens
to form a virtual image on the human eye retina, as shown in Figure 1.2. The virtual
image is inverted with respect to the object. The virtual image is often adjusted to
be located as the minimum distance of eye focus, which is conventionally taken
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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1
1 Light Microscopy
C
A
B
Final image
Object
1st image
f1
Figure 1.1
f1
f2
f2
Principles of magnification in a microscope.
Eyepiece
Objective
Object
Eye Lens
Final image
Primary image
Retina
Virtual image
250 mm
Figure 1.2 Schematic path of light in a microscope with an eyepiece. The virtual image is
reviewed by a human eye composed of the eye lens and retina.
as 250 mm from the eyepiece. A modern microscope is commonly equipped with
a device to switch from eyepiece to projector lens for either recording images on
photographic film or sending images to a computer screen.
Advanced microscopes made since 1980 have a more complicated optical arrangement called ‘‘infinity-corrected’’ optics. The objective lens of these microscopes
generates parallel beams from a point on the object. A tube lens is added between
the objective and eyepiece to focus the parallel beams to form an image on a plane,
which is further viewed and enlarged by the eyepiece.
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2
The magnification of a microscope can be calculated by linear optics, which tells
us the magnification of a convergent lens, M:
M=
v−f
f
(1.1)
where f is the focal length of the lens and v is the distance between the image and
lens. A higher magnification lens has a shorter focal length, as indicated by Eq.
(1.1). The total magnification of a compound microscope as shown in Figure 1.1
should be the magnification of the objective lens multiplied by that of the projector
lens.
M = M1 M2
(v1 − f1 )(v2 − f2 )
f1 f2
(1.2)
When an eyepiece is used, the total magnification should be the objective lens
magnification multiplied by the eyepiece magnification.
1.1.2
Resolution
We naturally ask whether there is any limitation for magnification in light microscopes because Eq. (1.2) suggests there is no limitation. However, meaningful
magnification of a light microscope is limited by its resolution. Resolution refers
to the minimum distance between two points at which they can be visibly distinguished as two points. The resolution of a microscope is theoretically controlled by
the diffraction of light.
Light diffraction controlling the resolution of microscope can be illustrated with
the images of two self-luminous point objects. When the point object is magnified,
its image is a central spot (the Airy disk) surrounded by a series of diffraction
rings (Figure 1.3), not a single spot. To distinguish between two such point objects
separated by a short distance, the Airy disks should not severely overlap each other.
Thus, controlling the size of the Airy disk is the key to controlling resolution. The
size of the Airy disk (d) is related to the wavelength of light (λ) and the angle
of light coming into the lens. The resolution of a microscope (R) is defined as the
minimum distance between two Airy disks that can be distinguished (Figure 1.4).
Resolution is a function of microscope parameters as shown in the following
equation:
R=
0.61λ
d
=
2
μ sin α
(1.3)
where μ is the refractive index of the medium between the object and objective lens
and α is the half-angle of the cone of light entering the objective lens (Figure 1.5).
The product, μ sin α, is called the numerical aperture (NA).
According to Eq. (1.3), to achieve higher resolution we should use shorterwavelength light and larger NA. The shortest wavelength of visible light is about
400 nm, while the NA of the lens depends on α and the medium between the
3
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1.1 Optical Principles
I
−2.23π −1.22π
1.22π
2.23π
π dsinφ
λ
Figure 1.3 A self-luminous point object and the light-intensity distribution along a line
passing through its center.
l1
l2
d /2
Figure 1.4 Intensity distribution of two airy disks with a distance d/2. I1 indicates the maximum intensity of each point and I2 represents the overlap intensity.
lens and object. Two media between object and objective lens are commonly used:
either air for which μ = 1, or oil for which μ ≈ 1.5. Thus, the maximum value of
NA is about 1.5. We estimate the best resolution of a light microscope from Eq.
(1.3) as about 0.2 μm.
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1 Light Microscopy
4
Aperture
α
Object
Optical axis
Objective lens
Figure 1.5 The cone of light entering an objective lens showing α is the half-angle.
1.1.2.1 Effective Magnification
Magnification is meaningful only in so far as the human eye can see the features
resolved by the microscope. Meaningful magnification is the magnification that is
sufficient to allow the eyes to see the microscopic features resolved by the microscope. A microscope should enlarge features to about 0.2 mm, the resolution level of
the human eye. This means that the microscope resolution multiplying the effective
magnification should be equal to the eye resolution. Thus, the effective magnification
of a light microscope should approximately be Meff = 0.2 ÷ 0.2 × 103 = 1.0 × 103 .
A higher magnification than the effective magnification only makes the image
bigger, may make eyes more comfortable during observation, but does not provide
more detail in an image.
1.1.2.2 Brightness and Contrast
To make a microscale object in a material specimen visible, high magnification is
not sufficient. A microscope should also generate sufficient brightness and contrast
of light from the object. Brightness refers to the intensity of light. In a transmission
light microscope the brightness is related to the numerical aperture (NA) and
magnification (M).
Brightness =
(NA)2
M2
(1.4)
In a reflected-light microscope the brightness is more highly dependent on NA.
Brightness =
(NA)4
M2
(1.5)
These relationships indicate that the brightness decreases rapidly with increasing
magnification, and controlling NA is not only important for resolution but also for
brightness, particularly in a reflected-light microscope.
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1.1 Optical Principles
1 Light Microscopy
Contrast is defined as the relative change in light intensity (I) between an object
and its background.
Contrast =
Iobject − Ibackground
(1.6)
Ibackground
Visibility requires that the contrast of an object exceeds a critical value called the
contrast threshold. The contrast threshold of an object is not constant for all images
but varies with image brightness. In bright light, the threshold can be as low as
about 3%, while in dim light the threshold is greater than 200%.
1.1.3
Depth of Field
Depth of field is an important concept when photographing an image. It refers to
the range of position for an object in which image sharpness does not change.
As illustrated in Figure 1.6, an object image is only accurately in focus when the
object lies in a plane within a certain distance from the objective lens. The image
is out of focus when the object lies either closer to or farther from the lens. Since
the diffraction effect limits the resolution R, it does not make any difference to the
sharpness of the image if the object is within the range of Df shown in Figure 1.6.
Thus, the depth of field can be calculated.
Df =
d
2R
1.22λ
=
=
tan α
tan α
μ sin α tan α
(1.7)
Equation (1.7) indicates that a large depth of field and high resolution cannot be
obtained simultaneously; thus, a larger Df means a larger R and worse resolution.
A
Aperture
d
α
Df
Focal plane
Figure 1.6 Geometric relation among the depth of field (Df ), the half-angle entering the
objective lens (α), and the size of the Airy disk (d).
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6
We may reduce angle α to obtain a better depth of field only at the expense of
resolution. For a light microscope, α is around 45◦ and the depth of field is about
the same as its resolution.
We should not confuse depth of field with depth of focus. Depth of focus refers
to the range of image plane positions at which the image can be viewed without
appearing out of focus for a fixed position of the object. In other words, it is the
range of screen positions in which and images can be projected in focus. The depth
of focus is M2 times larger than the depth of field.
1.1.4
Aberrations
The aforementioned calculations of resolution and depth of field are based on
the assumptions that all components of the microscope are perfect, and that light
rays from any point on an object focus on a correspondingly unique point in the
image. Unfortunately, this is almost impossible due to image distortions by the
lens called lens aberrations. Some aberrations affect the whole field of the image
(chromatic and spherical aberrations), while others affect only off-axis points of the
image (astigmatism and curvature of field). The true resolution and depth of field
can be severely diminished by lens aberrations. Thus, it is important for us to have
a basic knowledge of aberrations in optical lenses.
Chromatic aberration is caused by the variation in the refractive index of the lens
in the range of light wavelengths (light dispersion). The refractive index of lens glass
is greater for shorter wavelengths (for example, blue) than for longer wavelengths
(for example, red). Thus, the degree of light deflection by a lens depends on
the wavelength of light. Because a range of wavelengths is present in ordinary
light (white light), light cannot be focused at a single point. This phenomenon is
illustrated in Figure 1.7.
Spherical aberration is caused by the spherical curvature of a lens. Light rays from
a point on the object on the optical axis enter a lens at different angles and cannot
Blue
Red
Optical axis
Red
Blue
Figure 1.7 Paths of rays in white light illustrating chromatic aberration.
7
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1.1 Optical Principles
1 Light Microscopy
be focused at a single point, as shown in Figure 1.8. The portion of the lens farthest
from the optical axis brings the rays to a focus nearer the lens than does the central
portion of the lens.
Astigmatism results when the rays passing through vertical diameters of the
lens are not focused on the same image plane as rays passing through horizontal
diameters, as shown in Figure 1.9. In this case, the image of a point becomes an
elliptical streak at either side of the best focal plane. Astigmatism can be severe in
a lens with asymmetric curvature.
Curvature of field is an off-axis aberration. It occurs because the focal plane of an
image is not flat but has a concave spherical surface, as shown in Figure 1.10. This
aberration is especially troublesome with a high magnification lens with a short
focal length. It may cause unsatisfactory photography.
There are a number of ways to compensate for and/or reduce lens aberrations.
For example, combining lenses with different shapes and refractive indices corrects
chromatic and spherical aberrations. Selecting single-wavelength illumination by
the use of filters helps eliminate chromatic aberrations. We expect that the extent
to which lens aberrations have been corrected is reflected in the cost of the lens. It
is a reason that we see huge price variation in microscopes.
Optical axis
Figure 1.8
Spherical aberration.
Optical axis
Figure 1.9
Astigmatism is an off-axis aberration.
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8
Figure 1.10 Curvature of field is an off-axis aberration.
1.2
Instrumentation
A light microscope includes the following main components:
•
•
•
•
•
illumination system;
objective lens;
eyepiece;
photomicrographic system; and
specimen stage.
A light microscope for examining material microstructure can use either transmitted or reflected light for illumination. Reflected-light microscopes are the most
commonly used for metallography, while transmitted-light microscopes are typically
used to examine transparent or semitransparent materials, such as certain types of
polymers. Figure 1.11 illustrates the structure of a light microscope for materials
examination.
1.2.1
Illumination System
The illumination system of a microscope provides visible light by which a specimen is observed. There are three main types of electric lamps used in light
microscopes:
1) low-voltage tungsten filament bulbs;
2) tungsten–halogen bulbs; and
3) gas-discharge tubes.
Tungsten bulbs provide light of a continuous wavelength spectrum from about
300 to 1500 nm. Their color temperature of the light, which is important for
color photography, is relatively low. Low color temperature implies warmer (more
yellow–red) light while high color temperature implies colder (more blue) light.
Tungsten–halogen bulbs, like ordinary tungsten bulbs, provide a continuous
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1.2 Instrumentation
1 Light Microscopy
Figure 1.11 An Olympus light microscope used for material examination. The microscope
includes transmission- and reflection-illumination systems. (This image is courtesy of Olympus Corporation.)
spectrum. Their light is brighter and the color temperature is significantly higher
than ordinary tungsten bulbs. The high filament temperature of tungsten–halogen
bulbs, however, needs a heat filter in the light path and good ventilation. Gasdischarge tubes filled with pressurized mercury or xenon vapor provide extremely
high brightness. The more commonly used tubes are filled with mercury, of which
the arc has a discontinuous spectrum. Xenon has a continuous spectrum and very
high color temperature. As with tungsten–halogen bulbs, cooling is required for
gas-discharge tubes.
In a modern microscope, the illumination system is composed of a light lamp
(commonly a tungsten–halogen bulb), a collector lens and a condenser lens to provide
integral illumination; such a system is known as the Köhler system. The main
feature of the Köhler system is that the light from the filament of a lamp is first
focused at the front focal plane of the condenser lens by a collector lens. Then,
the condenser lens collects the light diverging from the source and directs it at
a small area of the specimen be examined. The Köhler system provides uniform
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10
Conjugate aperture planes
Conjugate field planes
Retina
Eye lens
Eyepiece
Primary image plane
Back focal plane
Objective lens
Specimen
Condenser lens
Aperture diaphragm
Field diaphragm
Collector lens
Lamp
Figure 1.12 Two sets of conjugate focal
planes in the Köhler system illustrated in a
transmitted-light microscope. Image-forming
rays focus on the field planes and illuminating rays focus on the aperture planes. The
far left-hand and far right-hand parts of the
diagram illustrate the images formed by
image-forming rays and illuminating rays,
respectively. (Reproduced with permission
from Ref. [1]. © 2001 John Wiley & Sons
Inc.)
intensity of illumination on the area of specimen. The system generates two sets of
conjugate focal planes along the optic axis of a microscope as shown in Figure 1.12.
One set of focal planes is for illuminating rays; these are known as the conjugate
aperture planes. Another set comprises the image-forming rays called the conjugate
field planes. During normal microscope operation, we see only the image-forming
rays through the eyepiece. We can use the illuminating rays to check the alignment
of the optical system of the microscope.
There are two important controllable diaphragms in the Köhler system: the field
diaphragm and the aperture diaphragm. The field diaphragm is placed at a focal
plane for the image-formation rays. Its function is to alter the diameter of the
illuminated area of the specimen. When the condenser is focused and centered, we
see a sharp image of the field diaphragm with the image of specimen (Figure 1.13).
The field diaphragm restricts the area of view and blocks scattering light that could
cause glare and image degradation if they entered the objective lens and eyepiece.
The aperture diaphragm is placed at a focus plane of the illuminating rays. Its
function is to control α, and thus affect the image resolution and depth of field
11
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1.2 Instrumentation
1 Light Microscopy
Figure 1.13
100×.
(a)
Image of the field diaphragm with an image of the specimen. Magnification
(b)
Figure 1.14 Effect of aperture diaphragm on specimen image when: (a) the aperture is
large and (b) the aperture is small. Magnification 500×.
(Sections 1.1.2 and 1.1.3). We cannot see the aperture diaphragm with the image
of specimen. Figure 1.14 illustrates the influence of the aperture diaphragm on the
image of a specimen.
The main difference between transmitted-light and reflected-light microscopes
is the illumination system. The Köhler system of reflected light illumination (epiillumination) is illustrated in Figure 1.15 in which a relay lens is included. The
illuminating rays are reflected by a semitransparent reflector to illuminate the
specimen through an objective lens. There is no difference in how reflected and
transmitted-light microscopes direct light rays after the rays leave the specimen.
There may be a difference in the relative position of the field and aperture
diaphragms (Figure 1.12). However, the field diaphragm is always on the focal
plane of the image-forming rays while the aperture diaphragm is on a focal plane
of the illuminating rays.
Light filters are often included in the light path of illumination systems, even
though they are not shown in Figures 1.12 and 1.15. Light filters are used to
control the wavelengths and intensity of illumination in microscopes in order to
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12
13
Eyepiece
Primary
image plane
Aperture
Diaphragm
Field
Diaphragm
Lamp
Back focal
plane
Objective
Relay lens
Condenser
Collector
Figure 1.15 Illumination system of a reflected-light microscope with illuminating rays.
achieve optimum visual examination for photomicrography. Neutral density (ND)
filters can regulate light intensity without changing wavelength. Colored filters and
interference filters are used to isolate specific colors or bands of wavelength. The
colored filters are commonly used to produce a broad band of color, while the
interference filters offer sharply defined bandwidths. Colored filters are used to
match the color temperature of the light to that required by photographic films.
Selected filters can also increase contrast between specimen areas with different
colors. Heat filters absorb much of the infrared radiation that causes heating of
specimen when a tungsten–halogen bulb is used as light source.
1.2.2
Objective Lens and Eyepiece
The objective lens is the most important optical component of a light microscope.
The magnification of the objective lens determines the total magnification of the
microscope because eyepieces commonly have a fixed magnification of 10×. The
objective lens generates the primary image of the specimen, and its resolution
determines the final resolution of the image. The numerical aperture (NA) of
the objective lens varies from 0.16 to 1.40, depending on the type of lens. A
lens with a high magnification has a higher NA. The highest NA for a dry lens
(where the medium between the lens and specimen is air) is about 0.95. Further
increase in NA can be achieved by using a lens immersed in an oil medium. The
oil-immersion lens is often used for examining microstructure greater than 1000×
magnification.
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1.2 Instrumentation
1 Light Microscopy
Classification of the objective lens is based on its aberration-correction capabilities, mainly chromatic aberration. The following lenses are shown from low to
high capability.
• achromat;
• semiachromat (also called ‘‘fluorite’’); and
• apochromat.
The achromatic lens corrects chromatic aberration for two wavelengths (red
and blue). It requires green illumination to achieve satisfactory results for visual
observation of black and white photography. The semiachromatic lens improves
correction of chromatic aberration. Its NA is larger than that of an achromatic lens
with the same magnification and produces a brighter image and higher resolution of
detail. The apochromatic lens provides the highest degree of aberration correction.
It almost completely eliminates chromatic aberration. It also provides correction
of spherical aberration for two colors. Its NA is even larger than that of a
semiachromatic lens. Improvement in quality requires a substantial increase in
the complexity of the lens structure, and costs. For example, an apochromatic lens
may contain 12 or more optical elements.
The characteristics of an objective lens are engraved on the barrel as shown in
Figure 1.16. Engraved markings may include the following abbreviations.
• ‘‘FL,’’ ‘‘FLUOR,’’ or ‘‘NEOFLUOR’’ stands for ‘‘fluorite’’ and indicates the lens
is semiachromatic;
• ‘‘APO’’ indicates that the lens is apochromatic;
• If neither of the above markings appears, then the lens is achromatic;
• ‘‘PLAN’’ or ‘‘PL’’ stands for ‘‘planar’’ and means the lens is corrected for curvature
of field, and thus generates a flat field of image;
Nikon
Plane fluor
Magnification
Application
Lens-image distance/
Coverslip thickness
(mm)
100 X/1.30 Oil
Numerical aperture/
Immersion medium
DIC H
∞/0.17 WD 0.20
Working distance
(mm)
Color-coded ring
for magnification
Figure 1.16 Engraved markings on the barrel of an objective lens. (Reproduced with permission from Ref. [1]. © 2001 John Wiley & Sons Inc.)
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14
• ‘‘DIC’’ means the lens includes a Wollaston prism for differential interference
contrast (Section 1.4.4);
• ‘‘PH’’ or ‘‘PHACO’’ means the lens has a phase ring for phase-contrast microscopy (Section 1.4.2); and
• ‘‘number/number’’ indicates magnification/numerical aperture. Thus, ‘‘40/0.75’’
means the lens has a magnification of 40× and a numerical aperture of 0.75.
The eyepiece is used to view the real primary image formed by the objective
lens. In some cases it also completes the correction of aberrations. The eyepiece
allows a glass disc with an etched graticule to be inserted into the optical path. The
graticule serves as a micrometer for measurement. The eyepiece has either a helical
thread or a sliding mount as a focusing mechanism. Importantly, the focusing
mechanism of an eyepiece provides a ‘‘parfocal’’ adjustment of the optics so that
the same focal plane examined by the eye will be in focus on the film plane of the
camera mounted on the microscope. Thus, focusing the eyepiece is a necessary
step before photographing images in a microscope.
We can summarize the methods for achieving optimum resolution and depth of
field in light microscopy. While both resolution and depth of field are crucial for
achieving high-quality images, one often is achieved at the expense of the other.
Thus, compromises must be made while using good judgment.
1.2.2.1
Steps for Optimum Resolution
•
•
•
•
•
•
•
use an objective lens with the highest NA possible;
use high magnification;
use an eyepiece compatible with the chosen objective lens;
use the shortest possible wavelength light;
keep the light system properly centered;
use oil immersion lenses if available;
adjust the field diaphragm for maximum contrast and the aperture diaphragm
for maximum resolution and contrast; and
• adjust brightness for best resolution.
1.2.2.2
Steps to Improve Depth of Field
• reduce NA by closing the aperture diaphragm, or use an objective lens with lower
NA;
• lower the magnification for a given NA;
• use a high-power eyepiece with a low-power, high- NA objective lens; and
• use the longest possible wavelength light.
1.3
Specimen Preparation
The microstructure of a material can only be viewed in a light microscope after
a specimen has been properly prepared. Metallurgists have developed extensive
15
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1.3 Specimen Preparation
1 Light Microscopy
techniques and accumulated knowledge of metal specimen preparations for over
a century. In principle, we can use these techniques to examine not only metallic
materials but also ceramics and polymers; in practice, certain modifications are
needed and a certain degree of caution must be exercised. The main steps of
specimen preparation for light microscopy include the following.
•
•
•
•
•
sectioning;
mounting;
grinding;
polishing; and
etching.
1.3.1
Sectioning
Sectioning serves two purposes: generating a cross section of the specimen to be
examined; and reducing the size of a specimen to be placed on a stage of a light
microscope, or reducing the size of a specimen to be embedded in mounting media
for further preparation processes. The main methods of sectioning are abrasive
cutting, electric discharge machining, and microtomy that is mainly for polymer
specimens.
1.3.1.1 Cutting
Abrasive cutting is the most commonly used method for sectioning materials.
Specimens are sectioned by a thin rotating disc in which abrasive particles are
supported by suitable media. The abrasive cutoff machine is commonly used
for sectioning a large sample. The machine sections the sample with a rapidly
rotating wheel made of an abrasive material, such as silicon carbide, and bonding
materials such as resin and rubber. The wheels are consumed in the sectioning
process. Abrasive cutting requires cooling media in order to reduce friction heat.
Friction heat can damage specimens and generate artifacts in the microstructure.
Commonly used cooling media consist of water-soluble oil and rust-inhibiting
chemicals. The abrasive cutoff machine can section large specimens quickly but
with poor precision.
More precise cutting can be achieved by a diamond saw or electric discharge
machine (EDM) (Figure 1.17). The diamond saw is a precision abrasive cutting
machine. It sections specimens with a cutting wheel made of tiny diamond particles
bonded to a metallic substrate. A cooling medium is also necessary for diamond
saw cutting. Electrically conductive materials can be sectioned by an EDM. Cutting
is accomplished by an electric discharge between an electrode and the specimen
submerged in a dielectric fluid. EDM is particularly useful for materials that are
difficult to section by abrasive cutting. EDM may produce significant changes at
the machined surface because the electric discharge melts the solid in the cutting
path. The solidified material along a machining path must be carefully removed
during further preparation processes.
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16
(a)
(b)
Figure 1.17 Specimen sectioning by: (a) wire cutting with electric discharging and (b) diamond saw sectioning.
1.3.1.2 Microtomy
Microtomy refers to sectioning materials with a knife. It is a common technique
in biological specimen preparation. It is also used to prepare soft materials such
as polymers and soft metals. Tool steel, tungsten carbide, glass, and diamond
are used as knife materials. A similar technique, ultramicrotomy, is widely used
for the preparation of biological and polymer specimens in transmission electron
microscopy. This topic is discussed in Chapter 3.
1.3.2
Mounting
Mounting refers to embedding specimens in mounting materials (commonly
thermosetting polymers) to give them a regular shape for further processing.
Mounting is not necessary for bulky specimens, but it is required for specimens
that are too small or oddly shaped to be handled or when the edge of a specimen
needs to be examined in transverse section. Mounting is popular now because
most automatic grinding and polishing machines require specimens to have a
cylindrical shape. There are two main types of mounting techniques: hot mounting
and cold mounting.
Hot mounting uses a hot-press equipment as shown in Figure 1.18. A specimen
is placed in the cylinder of a press and embedded in polymeric powder. The surface
Heating
element
Hot press
power
Specimen
Figure 1.18 Internal arrangement of a hot mounting press.
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1.3 Specimen Preparation
1 Light Microscopy
to be examined faces the bottom of the cylinder. Then, the specimen and powder
are heated at about 150 ◦ C under constant pressure for tens of minutes. Heat
and pressure enable the powder to bond with the specimen to form a cylinder.
Phenolic (bakelite) is the most widely used polymeric powder for hot mounting.
Hot mounting is suitable for most metal specimens. However, if the microstructure
of the material changes at the mounting temperature, cold mounting should be
used.
In cold mounting, a polymer resin, commonly epoxy, is used to cast a mold
with the specimen at ambient temperature. Figure 1.19a shows a typical mold and
specimens for cold mounting. Figure 1.19b demonstrates the casting of epoxy resin
into the mold in which the specimen surface to be examined is facing the bottom. A
cold mounting medium has two constituents: a fluid resin and a powder hardener.
The resin and hardener should be carefully mixed in proportion following the
instructions provided. Curing times for mounting materials vary from tens of
minutes to several hours, depending on the resin type. Figure 1.20 shows the
specimens after being cold mounted in various resins.
An important issue in the selection of a mounting material is hardness compatibility with the specimen. Generally, plastics used for embedding are not as hard
as the specimen, particularly when the specimens are of metallic or ceramic. Too
great a difference in hardness can cause inhomogeneous grinding and polishing,
which in turn may generate a rough, rather than sharp edge on the specimen. A
solution to this problem is to embed metal beads with a specimen to ensure that
the grinding surface has a more uniform hardness.
There are a number of other mounting techniques available but they are less
widely used. The simplest is mechanical clamping, in which a thin sheet of the
specimen is clamped in place with a mechanical device. Adhesive mounting is
glueing a specimen to a large holder. Vacuum impregnation is a useful mounting
method for porous specimens and ceramics. It removes air from the pores, crevices,
and cracks of specimens, and then replaces such empty space in the specimen with
epoxy resin. First, a specimen is ground with grit paper to flatten the surface to
(a)
(b)
Figure 1.19 Cold mounting of specimens: (a) place specimens on the bottom of molds
supported by clamps and (b) cast resin into the mold. (Reproduced with permission of
Struers A/S.)
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18
(a)
(b)
(c)
Figure 1.20 Cold mounted specimens: (a) mounted with polyester; (b) mounted with
acrylic; and (c) mounted with acrylic and mineral fillers. (Reproduced with permission of
Struers A/S.)
be examined. The specimen is placed with the surface uppermost inside the mold
in a vacuum chamber. Then, the chamber is evacuated for several minutes before
filling the mold with epoxy. The vacuum is maintained for a few minutes and then
air is allowed to enter the chamber for a curing period.
1.3.3
Grinding and Polishing
Grinding refers to flattening the surface to be examined and removing any damage
caused by sectioning. The specimen surface to be examined is abraded using a
graded sequence of abrasives, starting with a coarse grit. Commonly, abrasives
(such as silicon carbide) are bonded to abrasive paper. Abrasive paper is graded
according to particle size of abrasives such as 120-, 240-, 320-, 400-, and 600-grit
paper. The starting grit size depends on the surface roughness and depth of damage
from sectioning. Usually, the starting grade is 240 or 320 grit after sectioning with
a diamond saw or EDM. Both hand grinding and machine grinding are commonly
used.
1.3.3.1 Grinding
We can perform hand grinding with a simple device in which four belts of abrasive paper (240-, 320-, 400-, and 600-grit) are mounted in parallel as shown in
Figure 1.21. Running water is supplied to cool specimen surfaces during hand
grinding. Grinding produces damage that must be minimized by subsequent grinding with finer abrasives. The procedure is illustrated in Figure 1.22. In particular,
two procedures must be followed to ensure optimal results. First, specimens are
rinsed with running water to remove surface debris before switching grinding belts;
and secondly, specimens are rotated 90◦ from the previous orientation. Rotation
ensures that grinding damage generated by a coarse grit is completely removed by
a subsequent finer grit. Thus, at the end of any grinding step, the only grinding
damage present must be from that grinding step. Damage from the final grinding
step is removed by polishing.
19
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1.3 Specimen Preparation
1 Light Microscopy
Figure 1.21 Hand grinding using a simple hand grinding device. (Reproduced with permission of Buehler Ltd.)
Water
rinsing
Water
rinsing
Water
rinsing
Grinding
direction
Polishing
240 grit
Figure 1.22
320 grit
400 grit
600 grit
Hand grinding procedure.
Automatic grinding machines have become very popular because they reduce
tedious work and are able to grind multiple specimens simultaneously. Also,
machine grinding produces more consistent results. A disc of abrasive paper is
held on the surface of a motor-driven wheel. Specimens are fixed on a holder
that also rotates during grinding. Modern grinding machines control the speeds
of the grinding wheel and the specimen holder independently. The direction of
rotation of the holder and the compressive force between specimen and grinding
wheel can also be altered. The machines usually use running water as the cooling
medium during grinding to avoid friction heat and to remove loose abrasives that
are produced continuously during grinding.
1.3.3.2 Polishing
Polishing is the last step in producing a flat, scratch-free surface. After being ground
to a 600-grit finish, the specimen should be further polished to remove all visible
scratches from grinding. Effects of grinding and polishing a specimen surface are
shown in Figure 1.23. Polishing generates a mirror-like finish on the specimen
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20
21
120 grit
240 grit
320 grit
400 grit
600 grit
6-μm diamond
1-μm diamond
Colloidal silica
Figure 1.23 Sample of specimen surfaces after grinding and polishing with abrasives of
different grits and size. (Reproduced with permission of ASM International®. All Rights Re®
served. www.asminternational.org. Ref. [2]. © 1984 ASM International .)
surface to be examined. Polishing is commonly conducted by placing the specimen
surface against a rotating wheel either by hand or by a motor-driven specimen
holder (Figure 1.24). Abrasives for polishing are usually diamond paste, alumina,
or other metal-oxide slurries. Polishing includes coarse and fine polishing. Coarse
polishing uses abrasives with a grit size in the range from 3 to 30 μm; 6-μm
diamond paste is the most popular. The abrasive size for fine polishing is usually
less than 1 μm. Alumina slurries provide a wide range of abrasive size, ranging
down to 0.05 μm.
A polishing cloth covers a polishing wheel to hold the abrasives against the
specimen during polishing. Polishing cloths must not contain any foreign matter
that may scratch specimen surfaces. Polishing cloths should also be able to retain
abrasives so that abrasives are not easily thrown out from the wheel. For coarse
polishing, canvas, nylon, and silk are commonly used as they have little or no nap.
For fine polishing, medium- or high-nap cloths are often used; one popular type
consists of densely packed, vertical synthetic fibers.
When hand polishing using a polishing wheel, we should not push the specimen
too hard against the wheel as excessive force will generate plastic deformation in
the top layer of a polished surface. We should also rotate the specimen against
the rotation direction of wheel. Without rotation, artifacts of comet tailing will
appear on the polished surfaces as shown in Figure 1.25. After each polishing step,
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1.3 Specimen Preparation
1 Light Microscopy
Figure 1.24 Polishing on a rotating wheel with a mechanical sample holder. (Reproduced
with permission of Struers A/S.)
(a)
(b)
Figure 1.25 Comet tailing generated by polishing on specimen surface: (a) bright-field image and (b) Nomarski contrast image. (Reproduced with permission of Struers A/S.)
the surface should be cleaned in running water with cotton or tissue, followed
by alcohol or hot-air drying. Alcohol provides fast drying of surfaces without
staining.
Electrolytic polishing is an alternative method of polishing metallic materials. A
metal specimen serves as the anode in an electrochemical cell containing an appropriate electrolyte. The surface is smoothed and brightened by the anodic reaction in
an electrochemical cell when the correct combination of bath temperature, voltage,
current density, and time are used. The advantage of this method over conventional
polishing is that there is no chance of plastic deformation during the polishing
surface. Plastic deformation in the surface layer of specimens can be generated
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22
by compression and shear forces arising from conventional polishing methods.
Plastic deformation from polishing may generate artifacts in microstructures of
materials.
The aforementioned methods of specimen preparation, except microtomy, are
regarded as an important part of metallography. These methods are also used
for nonmetallic materials such as ceramics, composites, and polymers. However,
various precautions must be taken in consideration of each material’s particular
characteristics. For example, ceramic materials are brittle. To avoid fracture they
should be mounted and sectioned with a slow-speed diamond saw. Composite
materials may exhibit significant differences in mechanical properties between the
reinforcement and matrix. These specimens require light pressure and copious
cooling during grinding and polishing. Polymeric materials can be examined by
either reflected or transmitted-light microscopes. For reflected-light microscopy,
specimen preparation is similar to that of metals. For transmitted-light microscopy,
a thin-section is required. Both surfaces of the thin section should be ground and
polished. This double-sided grinding and polishing can be done by mounting the
specimen in epoxy, preparing one surface, mounting that polished surface on a
glass slide, and finally grinding and polishing the other side.
1.3.4
Etching
Chemical etching is a method to generate contrast between microstructural features in specimen surfaces. Etching is a controlled corrosion process by electrolytic
action between surface areas with differences in electrochemical potential. Electrolytic activity results from local physical or chemical heterogeneities that render
some microstructural features anodic and others cathodic under specific etching
conditions. During etching, chemicals (etchants) selectively dissolve certain areas of the specimen surface because such areas exhibit different electrochemical
potentials and will serve as the anode in an electrochemical reaction on the specimen surface. For example, grain boundaries in polycrystalline materials are more
severely attacked by etchant, and thus are revealed by light microscopy because
they reflect light differently, as illustrated in Figure 1.26a and appear as the dark
lines shown in Figure 1.26b. Also, grains are etched at different rates because of
differences in grain orientation (certain crystallographic planes are more subject to
etching), resulting in crystal faceting. Thus, the grains show different brightness.
Etching a specimen that has a multiphase microstructure will result in selective
dissolution of the phases.
Many chemical etchants are mixtures of acids with a solvent such as water. Acids oxidize atoms of a specimen surface and change them to cations.
Electrons released from atoms of specimen surfaces are combined with hydrogen to form hydrogen gas. For more noble materials, etchants must contain
oxidizers (such as nitric acid, chromic acid, iron chloride, and peroxides). Oxidizers release oxygen, which accepts electrons from atoms of the specimen
23
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1.3 Specimen Preparation
1 Light Microscopy
Polished and
etched surface
Surface
groove
Grain boundary
Figure 1.26 Contrast generated by etching grain boundaries in light microscope: (a) reflection from different parts of a surface (Reproduced with permission from Ref. [3]. © 2006
John Wiley & Sons Inc.) and (b) micrograph of grain boundaries that appear as dark lines.
(Contribution of the National Institute of Standards and Technology.)
surface. Table 1.1 lists some commonly used etchants, their compositions and
applications.
Etching can simply be performed by immersion or swabbing. For immersion
etching, the specimen is immersed in a suitable etchant solution for several
seconds to several minutes, and then rinsed with running water. The specimen
should be gently agitated to eliminate adherent air bubbles during immersion.
For swab etching, the polished surface of a specimen is wiped with a soft cotton
swab saturated with etchant. Etching can also be assisted with direct electric
current, similar to an electrolytic polishing, using the specimen as an anode and
an insoluble material (such as platinum) as the cathode in an electrochemical
cell filled with electrolyte. The electrochemical reaction on the anode produces
selective etching on the specimen surface. Since electrochemical etching is a
chemical reaction, besides choosing a suitable etchant and electrolyte, temperature
and time are the key parameters to avoiding underetching and overetching of
specimens.
We may also use the method of tint etching to produce color contrast in
microstructures. Tint etchants, usually acidic, are able to deposit a thin (40–500 nm)
film such as an oxide or sulfide on specimen surfaces. Tint etching requires a very
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24
Table 1.1
Common etchants for light microscopy.
Materials
Compositiona
Procedure
Al and alloys
Keller’s reagent
2.5 ml HNO3 , 1.5 ml HCl
1.0 ml HF, 95 ml water
Immerse 10–20 s
Fe and steels
Nital
Immerse few seconds to 1 min
Fe and steels
1–10 ml HNO3 in 90–99 ml
methanol Picral
4–10 g picric acid, 100 ml
ethanol Vilella’s Reagent
1 g picric acid, 5 ml HCl, 100 ml
ethanal
2 g K2 Cr2 O7 , 8 ml H2 SO4 , 4
drops HCl, 100 ml water
Immerse few seconds to 1 min
10 ml HF, 5 ml HNO3 , 85 ml
water
1 ml HNO3 , 75 ml ethylene
glycol, 25 ml water
Palmerton’s Reagent
Swab 3–20 s
Stainless steels
Cu and alloys
Ti and alloys
Mg and alloys
Zn and alloys
Co and alloys
Ni and alloys
Immerse for up to 1 min
Add the HCl before using;
immerse 3–60 s
Swab 3–120 s
Immerse up to 3 min; rinse in
20% aq. CrO3
40 g CrO3 , 3 g Na2 SO4 , 200 ml
water
15 ml HNO3 , 15 ml acetic acid, Age 1 h before use; immerse for
60 ml HCl, 15 ml water
up to 30 s
50 ml HNO3 , 50 ml acetic acid
Immerse or swab 5–30 s; use
hood, do not store
Al2 O3
15 ml water, 85 ml H3 PO4
Boil 1–5 min
CaO and MgO
Concentrated HCl
Immerse 3 s to a few minutes
CeO2 , SrTiO3 , Al2 O3 , and
ZrO–ZrC
Si3 N4
20 ml water, 20 ml HNO3 , 10 ml Immerse up to 15 min
HF
Molten KOH
Immerse 1–8 min
SiC
10 g NaOH, 10 g K3 Fe(CN)6 in
100 ml water at 110 ◦ C
Xylene
Polyethylene (PE)
Poly(acrylonitrile butadiene 400 ml H2 SO4 , 130 ml H3 PO4 ,
styrene) (ABS); high-impact 125 ml water, 20 g CrO3
polystyrene (HIPS); and
poly(phenylene oxide) (PPO)
Polypropylene (PP)
6 M CrO3
Phenol formaldehyde
a
Boil to dryness
Immerse 1 min at 70 ◦ C
Immerse 15–180 s
Immerse 96 h at 70 ◦ C
75 ml dimethyl sulfoxide, 25 ml Immerse 4 h at 75–80 ◦ C
HNO3
The names of reagents are given in italics.
25
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1.3 Specimen Preparation
1 Light Microscopy
high-quality polished surface for best results. Tint etching can also be done by heat
tinting, a process by which a specimen is heated to a relatively low temperature in
air. As it warms, the polished surface is oxidized. The oxidation rate varies with
the phase and chemical composition of the specimen. Thus, differences in the
thickness of oxidation films on surfaces generate variations in color. Interference
colors are obtained once the film reaches a certain thickness. The effectiveness
of heat tinting depends on the material of specimens: it is effective for alloy
steels and other nonferrous metals and carbides, but not for carbon or low-alloy
steels.
1.4
Imaging Modes
The differences in properties of the light waves reflected from microscopic objects enable us to observe these objects by light microscopy. The light wave
changes in either amplitude or phase when it interacts with an object as illustrated in Figure 1.27. The eye can only appreciate amplitude and wavelength
differences in light waves, not their phase difference. The most commonly used
examination modes, bright-field and dark-field imaging, are based on contrast due
to differences in wave amplitudes. The wave phase differences have to be converted to amplitude differences through special optical arrangements such as in
the examination modes of phase contrast, polarized light, and Nomarski contrast.
This section introduces commonly used modes of light microscopy for materials
characterization.
1.4.1
Bright-Field and Dark-Field Imaging
Bright-field imaging is the predominant mode for examining microstructure. Darkfield imaging is also widely used to obtain an image with higher contrast than in
(a)
Reference
wave
(b)
Amplitude
object
Reduced
amplitude
(c)
Phase
object
Retarded
phase
Figure 1.27 (a) Reference wave; (b) amplitude difference; and (c) phase difference generated by objects. (Reproduced with permission from Ref. [1]. © 2001 John Wiley & Sons
Inc.)
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26
Objective
Object
Condenser
Aperture
(a)
(b)
Annular stop-IRIS
Central stop
Figure 1.28 (a) Bright-field illumination and (b) dark-field illumination in transmitted
mode. Shaded areas indicate where the light is blocked.
bright-field imaging. Figure 1.28 illustrates the difference in optical arrangement
between these modes in transmitted illumination. In bright-field imaging, the
specimen is evenly illuminated by a light source. Dark-field imaging requires that
the specimen is illuminated by oblique light rays. There is a central stop in the
light path to block the central portion of light rays from illuminating the specimen
directly. Thus, the angle of the light rays illuminating the specimen is so large
that light from the specimen cannot enter the objective lens unless it is scattered
by microscopic objects. The dark field in reflected illumination is also realized
using a central stop in the light path (Figure 1.29), similar to that of transmitted
illumination. The light rays in a ring shape will be further reflected in order
to illuminate a specimen surface with an oblique angle. Figure 1.30 shows the
comparison between bright- and dark-field images of an identical field in a highcarbon steel specimen under a reflected-light microscope. Microscopic features
such as grain boundaries and second-phase particles appear self-luminous in the
dark-field image, as shown in Figure 1.30.
1.4.2
Phase-Contrast Microscopy
Phase contrast is a useful technique for specimens such as polymers that have little
inherent contrast in the bright-field mode. In the technique, a phase change due to
27
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1.4 Imaging Modes
1 Light Microscopy
Central stop
Figure 1.29
Dark-field illumination in a reflected-light microscope.
(a)
Figure 1.30 Comparison between: (a)
bright-field and (b) dark-field images of
AISI 1080 high carbon steel. In addition to
grain boundaries and oxide particles, annealing twins are revealed in the dark-field
(b)
image. (Reproduced with permission of
ASM International®. All Rights Reserved.
www.asminternational.org. Ref. [2]. © 1984
®
ASM International .)
light diffraction by an object is converted to an amplitude change. This conversion
is based on interference phenomenon of light waves as illustrated in Figure 1.31.
Constructive interference occurs when combining two same-wavelength waves that
do not have a phase difference between them. However, completely destructive
interference occurs when combining two waves with a phase difference of a
half-wavelength λ2 .
Figure 1.32 illustrates generation of phase contrast by a special optical
arrangement in a transmitted-light microscope. This optical arrangement creates
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28
O
Wave 1
λ
Scattering Wave 1
event
λ
Amplitude
A
λ
λ
A
O′
P
Amplitude
Wave 2′
Scattering
event
Wave 3′
λ
A
A
A
+
λ
A
(b)
2A
Position
Wave 3
λ
P′
+
A
Wave 2
(a)
λ
A
A
λ
Wave 4
Wave 4′
Position
Figure 1.31 Illustration interference between waves: (a) constructive interference and (b)
completely destructive interference. (Reproduced with permission from Ref. [3]. © 2006 John
Wiley & Sons Inc.)
completely destructive interference when light is diffracted by an object in the
specimen. A condenser annulus, an opaque black plate with a transparent ring,
is placed in the front focal plane of the condenser lens. Thus, the specimen is
illuminated by light beams emanating from a ring. The light beam that passes
through a specimen without diffraction by an object (the straight-through light
beam) will pass the ring of a phase plate placed at the back focal plane of the
objective lens. The phase plate is a plate of glass with an etched ring of reduced
thickness. The ring with reduced thickness in the phase plate enables the waves of
the straight-through beam to be advanced by λ4 . The light beam diffracted by the
object in the specimen cannot pass through the ring of the phase plate but only
through the other areas of the phase plate. If the diffracted beam is delayed by λ4
while passing through the object, a total λ2 difference in phase is generated.
When the straight-through beam and diffracted beam recombine at the image
plane, completely destructive interference occurs. Thus, we expect a dark image
of the object in phase-contrast microscopy. Variation in phase retardation across
29
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1.4 Imaging Modes
1 Light Microscopy
Image plane
Diffracted
light
Phase plate
Nondiffracted
light
Objective
Condenser
Condenser
annulus
Figure 1.32 Optical arrangement of phase-contrast microscopy. Shading marks the paths
of diffracted light. (Reproduced with permission from Ref. [1]. © 2001 John Wiley & Sons
Inc.)
the specimen produces variations in contrast. Figure 1.33 shows image differences
between bright-field and phase-contrast images of composites in transmitted-light
microscopy. In reflected-light microscopy, phase contrast can also be created
with a condenser annulus and phase plate similar to those in transmitted-light
microscopy.
1.4.3
Polarized-Light Microscopy
Polarized light is used to examine specimens exhibiting optical anisotropy. Optical anisotropy arises when materials transmit or reflect light with different
velocities in different directions. Most materials exhibiting optical anisotropy
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30
10 μm
(a)
(b)
Figure 1.33 Comparison of light transmission images of glass-fiber-reinforced polyamide
in: (a) bright-field and (b) phase-contrast modes. (Reproduced with kind permission of
Springer Science and Business Media from Ref. [4]. © 1996 Springer Science.)
Filter
Random
incident light
Polarized
transmitted
light
Figure 1.34 Formation of plane-polarized light by a polarizing filter. (Reproduced with
permission from Ref. [1]. © 2001 John Wiley & Sons Inc.)
have a noncubic crystal structure. Light, as an electromagnetic wave, vibrates in
all directions perpendicular to the direction of propagation. If light waves pass
through a polarizing filter, called a polarizer, the transmitted wave will vibrate
in a single plane as illustrated in Figure 1.34. Such light is referred to as planepolarized light. When polarized light is transmitted or reflected by anisotropic
material, the polarized light vibrates in a different plane from the incident
plane. Such polarization changes generate the contrast associated with anisotropic
materials.
Figure 1.35 illustrates the interaction between polarized light and an anisotropic
object. For a transparent crystal, the optical anisotropy is called double refraction or
birefringence, because refractive indices are different in two perpendicular directions
of the crystal. When a polarized light ray hits a birefringent crystal, the light ray is
split into two polarized light waves (ordinary wave and extraordinary wave) vibrating
in two planes perpendicular to each other. Because there are two refractive indices,
31
10 μm
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1.4 Imaging Modes
1 Light Microscopy
Low R.I direction
High R.I direction
Plane-polarized
wave
Ordinary
wave
Extraordinary
wave
Birefringent crystal
Ordinary wave
Extraordinary
wave
Phase difference
Figure 1.35 Interaction between plane-polarized light and a birefringent object. Two planepolarized light waves with a phase difference are generated by the materials. RI, refractive
index.
E Wave
O Wave
Figure 1.36 Resultant polarized light by vector addition of two plane-polarized light waves
from a birefringent object, the ordinary (O) wave and extraordinary (E) wave. (Reproduced
with permission from Ref. [1]. © 2001 John Wiley & Sons Inc.)
the two split light rays travel at different velocities, and thus exhibit a phase
difference. These two rays, with a phase difference vibrating in two perpendicular
planes, produce resultant polarized light because the electric vectors of their waves
are added (Figure 1.36). The resultant polarized light is called elliptically polarized
light because the projection of resultant vectors in a plane is elliptical.
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32
If the two polarized-light waves with equal amplitude have a phase difference of
the projection of resultant light is a spiraling circle. If the two polarized-light
waves with equal amplitude have a phase difference of λ2 , the projection of
resultant light is linear (45◦ from two perpendicular directions of polarized-light
wave planes). If the two polarized-light waves have another phase difference, the
projection of the resultant ray is a spiraling ellipse.
Differences in the resultant light can be detected by another polarizing filter
called an analyzer. Both polarizer and analyzer can only allow plane-polarized light
to be transmitted. The analyzer has a different orientation of polarization plane with
respect to that of the polarizer. Figure 1.37 illustrates the amplitude of elliptically
polarized light in a two-dimensional plane and the light amplitude passing through
an analyzer that is placed 90◦ with respect to the polarizer (called the crossed position
of the polarizer and analyzer).
Anisotropic materials are readily identified by exposure to polarized light because
their images can be observed with the polarizer and analyzer in the crossed
position. Such situations are illustrated in Figure 1.37 as the phase difference
between ordinary and extraordinary wave are not equal to zero nor to mλ (m is
an integer). Understandably, when examining anisotropic materials with polarized
light, rotation of the analyzer through 360◦ will generate two positions of maximum
and two positions of minimum light intensity.
Polarized light can enhance the contrast of anisotropic materials, particularly
when they are difficult to etch. It can also determine the optical axis, demonstrate
pleochroism (showing different colors in different directions) and examine the
thickness of anisotropic coatings from its cross sections. Figure 1.38 demonstrates
λ
,
4
0
Analyzer
0 or mλ λ/8
λ/4
3λ /8
λ /2
5λ /8
3λ /4 7λ /8
Polarizer
Figure 1.37 Intensity change of polarized light passing through an analyzer when the elliptically polarized light changes. The polarizer and analyzer are in a crossed position. (Reproduced with permission from Ref. [1]. © 2001 John Wiley & Sons Inc.)
33
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1.4 Imaging Modes
1 Light Microscopy
(a)
(b)
Figure 1.38 Example of using polarized-light microscopy for pure titanium specimen: (a)
bright-field image and (b) polarized-light image in which grains are revealed. (Reproduced
from Ref. [2]. © N. Gendron, General Electric Co.)
that polarized light reveals the grains of pure titanium, which cannot be seen in
the bright-field mode. Figure 1.39 shows a polarized-light micrograph of highdensity polyethylene (HDPE) that has been crystallized. Polarized light revealed
fine spherulite structures caused by crystallization.
An isotropic material (either with cubic crystal structure or amorphous) cannot
change the plane orientation of polarizing light. When a polarized light wave leaves
the material and passes through the analyzer in a crossed position, the light will
be extinguished. This situation is equivalent to the case of a resultant ray having a
phase difference of zero or mλ. However, isotropic materials can be examined in
the polarized-light mode when optical anisotropy is introduced into the materials
or on their surfaces. For example, if an isotropic transparent crystal is elastically
80 μm
Figure 1.39 Polarized-light micrograph of crystallized high-density polyethylene (HDPE).
(Reproduced with permission from Ref. [5]. © 2000 John Wiley & Sons Ltd.)
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34
deformed, it becomes optically anisotropic. A thick oxide film on isotropic metals
also makes them sensitive to the direction of polarized light because of double
reflection from surface irregularities in the film.
1.4.4
Nomarski Microscopy
ed
itt
d
an
Tr
oc
Bl
sm
ke
ke
Bl
oc
Analyzer
d
Nomarski microscopy is an examination mode using diffraction interference
contrast, DIC. The images that DIC produces are deceptively three-dimensional
with apparent shadows and a relief-like appearance. Nomarski microscopy also uses
polarized light with the polarizer and the analyzer arranged as in the polarized-light
mode. In addition, double quartz prisms (Wollaston prisms or DIC prisms) are used
to split polarized light and generate a phase difference.
The working principles of Nomarski microscopy can be illustrated using the light
path in a transmitted-light microscope as illustrated in Figure 1.40. The first DIC
Resultant
waveform
Wollaston II
Phase
object
(a)
(b)
(c)
Figure 1.40 Nomarski contrast generation
using polarized light. The first differential interference contrast (DIC) prism (not shown)
generates two parallel polarized beams illuminating the specimen. The second DIC
prism recombines two beams. Elliptically
polarized light is generated by the second
DIC prism when a phase difference between
the two beams is induced by an object: (a)
both polarized beams do not pass through a
phase object; (b) both beams pass through a
phase object; and (c) one of the two beams
passes through a phase object. (Reproduced
with permission from Ref. [1]. © 2001 John
Wiley & Sons Inc.)
35
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1.4 Imaging Modes
1 Light Microscopy
prism is placed behind the polarizer and in front of the condenser lens, and the
second DIC prism is placed behind the objective lens and in front of the analyzer.
The two beams created by the prism interfere coherently in the image plane and
produce two slightly displaced images differing in phase, thus producing height
contrast. The first DIC prism splits the polarized-light beam from the polarizer
into two parallel beams traveling along different physical paths. If a specimen
does not generate a path difference between the two parallel beams as shown by
two left-side beam pairs in Figure 1.40, the second DIC prism recombines the
pairs and produces linearly polarized light with the same polarization plane as it
was before it was split by the first DIC prism. Thus, the analyzer in the crossed
position with a polarizer will block light transmission. However, if a specimen
generates a path difference in a pair of beams, as shown by the right-side beam
pair, the recombined pair produced by the second DIC prism will be elliptically
polarized light. The analyzer cannot block such light and a bright area will be
visible.
The optical arrangement of Nomarski microscopy in a reflected-light microscope
is similar to that of a transmitted-light microscope, except that there is only one
DIC prism serving both functions of splitting the incident beam and recombining
reflected beams as illustrated in Figure 1.41. The DIC prism is commonly integrated
in the barrel of the objective lens, indicated by ‘‘DIC’’ marked on the barrel surface
(Section 1.2.2).
Figure 1.42 compares bright-field and Nomarski images using a carbon steel
specimen as an example. Contrast enhancements are achieved in the Nomarski
7
6
1 2
3
4
5
Figure 1.41 Optical arrangement of Nomarski microscopy in reflected light illumination. 1,
polarizer; 2, λ2 -plate; 3, DIC prism; 4, objective lens; 5, specimen; 6, light reflector; and 7,
analyzer.
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36
20 μm
(a)
20 μm
(b)
Figure 1.42 Effects of Nomarski contrast on carbon steel micrographs: (a) bright field and
(b) Nomarski contrast of the same field. (Reproduced with permission of Gonde Kiessler.)
micrographs. The Nomarski image appears three-dimensional and illuminated by
a low-angle light source. However, the image does not necessarily represent real
topographic features of a surface because the shadows and highlights that result
from phase differences may not correspond to low and high relief on the surface,
particularly in transmitted-light microscopy. The reason for this is that the phase
differences generated in Nomarski microscopy may result from differences either
in the optical path or in refractive index.
1.4.5
Fluorescence Microscopy
Fluorescence microscopy is useful for examining objects that emit fluorescent
light. Fluorescence is an optical phenomenon; it occurs when an object emits
light of a given wavelength when excited by incident light. The incident light
must have sufficient energy, that is, a shorter wavelength than that light emitting
from the object, to excite fluorescence. While only a small number of materials
exhibit this capability, certain types of materials can be stained with fluorescent
dyes (fluorochromes). The fluorochromes can selectively dye certain constituents
in materials, called fluorescent labeling. Fluorescent labeling is widely used for
polymeric and biological samples.
Fluorescence microscopy can be performed by either transmitted or reflected
illumination (epi-illumination). Reflected light is more commonly used because it
entails less loss of excited fluorescence than transmitted light. Figure 1.43 illustrates
the optical arrangement for fluorescence microscopy with epi-illumination. A
high-pressure mercury or xenon light can be used for generating high-intensity,
short-wavelength light. The light source should be ultraviolet, violet, or blue,
depending on the types of fluorochromes used in the specimen. A fluorescence
filter set, arranged in a cube as shown in Figure 1.43, includes an exciter filter,
dichroic mirror, and a barrier filter. The exciter filter selectively transmits a band
of short wavelengths for exciting a specific fluorochrome, while blocking other
wavelengths. The dichroic mirror reflects short-wavelength light to the objective
37
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1.4 Imaging Modes
1 Light Microscopy
Barrier or
emission filter
Exciter
filter
Dichroic mirror
Light
source
Filter cube
Objective
Object
Figure 1.43 Optical arrangement for fluorescence microscopy with epi-illumination. The
dotted line indicates the path of excitation light, and the solid line indicates the path of fluorescent light. (Reproduced with permission from Ref. [1]. © 2001 John Wiley & Sons Inc.)
(a)
(b)
Figure 1.44 Micrographs of asphalt–polyolefin elastomer (POE) blend obtained with
transmitted-light microscopy: (a) bright-field image that cannot reveal the two phases in
the blend and (b) a fluorescence-labeled image that reveals two-phase morphology. (Reproduced with permission of Jingshen Wu.)
lens and specimen, and also transmits returning fluorescent light toward the barrier
filter. The barrier filter transmits excited fluorescent light only, by blocking other
short-wavelength light. Figure 1.44 shows an example of fluorescence microscopy
used for examining a polymer blend. Fluorescence labeling reveals the dispersed
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38
polymer particles in an asphalt matrix, which cannot be seen in the bright-field
image.
1.5
Confocal Microscopy
Confocal microscopy is a related new technique that provides three-dimensional
(3D) optical resolution. Image formation in a confocal microscope is significantly
different from a conventional light microscope. Compared with a conventional
compound microscope, a modern confocal microscope has two distinctive features in its structure: a laser light source and a scanning device. Thus, the
confocal microscope is often referred to as the confocal laser scanning microscope
(CLSM). The laser light provides a high-intensity beam to generate image signals from individual microscopic spots in the specimen. The scanning device
moves the beam in a rectangular area of specimen to construct a 3D image on a
computer.
1.5.1
Working Principles
The optical principles of confocal microscopy can be understood by examining the
CLSM optical path that has reflected illumination as illustrated in Figure 1.45. The
laser beam is focused as an intense spot on a certain focal plane of the specimen
by a condenser lens, which also serves as an objective lens to collect the reflected
beam. A pinhole aperture is placed at a confocal plane in front of the light detector.
The reflected beam from the focal plane in a specimen becomes a focused point
at the confocal plane. The pinhole aperture blocks the reflected light from the
out-of-focal plane from entering the detector. Only the light signals from the focal
point in the specimen are recorded each time. Since the pinhole aperture can block
a large amount of reflected light, high-intensity laser illumination is necessary to
ensure that sufficient signals are received by the detector. The detector is commonly
a photomultiplier tube (PMT) that converts light signals to electric signals for image
processing in a computer.
To acquire an image of the focal plane, the plane has to be scanned in its two
lateral directions (x–y directions). To acquire a 3D image of a specimen, the plane
images at different vertical positions should also be recorded. A scanning device
moves the focal laser spot in the x–y directions on the plane in a regular pattern
called a raster. After finishing one scanning plane, the focal spot is moved in the
vertical direction to scan the next parallel plane.
Figure 1.46 illustrates two different methods of scanning in CLSM: specimen
and laser scanning. Specimen scanning was used in early confocal microscopes.
The specimen moves with respect to the focal spot and the optical arrangement
is kept stationary, as shown in Figure 1.46a. The beam is always located at the
39
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1.5 Confocal Microscopy
1 Light Microscopy
Detector
Pinhole aperture
Dichroic
mirror
Laser
point source
Objective lens
Focal plane
Specimen
Figure 1.45 Optical path in the confocal microscope. (Reproduced with permission from
Ref. [1]. © 2001 John Wiley & Sons Inc.)
optical axis in the microscope so that optical aberration is minimized. The main
drawback of this method is the low scanning speed. Laser scanning is realized
by two scanning mirrors rotating along mutually perpendicular axes as shown
in Figure 1.46b. The scan mirror can move the focal spot in the specimen by
sensitively changing the reflecting angle of the mirror. Changing the vertical
position of the spot is still achieved by moving the specimen in the laser-scanning
method.
The resolution of the confocal microscope is mainly determined by the size
of the focal spot of the laser beam. High spatial resolution of about 0.2 μm can
be achieved. A 3D image of specimen with thickness of up to 200 μm is also
achievable, depending on the opacity of specimen. Most confocal microscopes
are the fluorescence type. The microscopic features under the specimen surface
are effectively revealed when they are labeled with fluorescent dyes. Therefore,
the major use of confocal microscopy is confocal fluorescence microscopy in
biology.
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40
Photodetector
Photodetector
Confocal
pinholes
Confocal
pinholes
Dichroic
mirror
Dichroic
mirror
Laser
Laser
Scan
mirror
Scan
mirror
On-axis
On-axis
Off-axis
Conjugate
planes
Entrance
pupil plane
(a)
(b)
Figure 1.46 Two scanning methods in the confocal microscope: (a) specimen scanning
and (b) laser scanning. (Reproduced with permission from Ref. [6]. © 2006 Michiel Müller.)
1.5.2
Three-Dimensional Images
The technique of confocal microscopy can be considered as optical sectioning.
A three-dimensional (3D) image is obtained by reconstructing a deck of plane
images. Figure 1.47 shows an example of how a 3D image is formed with confocal
fluorescence microscopy. A biological specimen, a Spathiphyllum pollen grain,
was fluorescently labeled with acridine orange. In total, 80 sections of the pollen
grain were imaged for 3D reconstruction. The vertical distance between sections
is 1.1 μm. Figure 1.47 shows 11 of 80 plane images and the reconstructed 3D
image.
Although its major applications are in biology, confocal microscopy can also be
used for examining the surface topography and internal structure of semitransparent materials. Figure 1.48 shows an example of using confocal fluorescent
microscopy to examine particulate penetration through an air filter made of polymer foam. The particulates were fluorescently labeled and their locations in the
polymer foam are revealed against the polymer-foam surfaces.
41
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1.5 Confocal Microscopy
1 Light Microscopy
20 μm
Figure 1.47 Confocal fluorescence micrographs of a Spathiphyllum pollen grain. The optical section sequence is from left to right and top to bottom. The bottom right image
is obtained by 3D reconstruction. (Reproduced with permission from Ref. [6]. © 2006
Michiel Müller.)
(a)
(b)
Figure 1.48 Confocal micrographs of polyurethane foam with labeled particulates: (a) highlights of particulates and (b) locations of particulates on the foam surfaces. The scale bar is
1 mm. (Reproduced with permission from Ref. [7]. © 2002 Woodhead Publishing Ltd.)
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42
Z
X
Y
Figure 1.49 3D confocal fluorescent micrograph of silica particles in low-density polyethylene. (Reproduced with permission from Ref. [7]. © 2002 Woodhead Publishing Ltd.)
Figure 1.49 shows an example of using confocal fluorescent microscopy to reveal
microscopic features in a specimen. The specimen is low-density polyethylene
(LDPE) containing fluorescently labeled silica particles. The particle size and distribution in the polymer matrix can be clearly revealed by 3D confocal microscopy.
Thus, confocal microscopy provides us a new dimension in light microscopy for
materials characterization, even though its applications in materials science are
not as broad as in biology.
Questions
1.1
1.2
Three rules govern light path for a simple lens:
1. A light ray passing through the center of a lens is not deviated.
2. A light ray parallel with optic axis will pass through the rear focal point.
3. A ray passing through the front focal point will be refracted in a
direction parallel to the axis. Sketch the light paths from object to
image in a single-lens system in the following situations.
a. a < f ; (b) a = f ; (c) 2f > a > f ; (d) a = 2f ; and (e) a > 2f , where a
is the distance of object from lens and f is the focal length of lens.
By this exercise, you may understand that 2f > a > f is necessary to
obtain a real magnified image.
The working distance between the specimen and objective lens is determined
by the magnifications of the lens. Estimate the difference in the working
distance for objective lenses with powers of 5×, 20×, and 50×.
43
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1.5 Confocal Microscopy
1 Light Microscopy
1.3 Calculate the resolution and the depth of field of the objective lenses of a
light microscope, listed below. The refractive index of vacuum is 1, and that
of air can be treated as 1. Assume blue light is used in the microscope.
Magnification/NA
5×/0.13
10×/0.25
20×/0.40
50×/0.70
100×/0.90.
1.4 To obtain a 400 magnification image we may choose a 40× objective lens
with a 10× projector lens, or a 20× objective lens with a 20× projector lens.
What are the differences in their image quality?
1.5 We often have a much worse resolution of a lens than the calculated one in
Question 1.3. Why?
1.6 Compare the resolution and depth of field of light microscopes and electron
microscopes. The wavelength of electrons is 0.0037 nm (100 kV) and the
angle α of an electron microscope is 0.1 rad.
1.7 One found that he/she cannot a focused micrograph of a specimen even
though he/she has observed a focused image of the specimen by looking
through eyepiece. Why?
1.8 We have samples of an annealed Al alloy and an annealed plain carbon steel
to be examined. The polishing area of the samples is about 5 mm × 3 mm.
• To avoid plastic deformation in the surface layer, what are the maximum compression forces that should be used for polishing the samples
of annealed Al alloy and plain carbon steel, respectively?
• If normal compression force cannot cause plastic deformation, what
kind of loading on the samples more likely causes plastic deformation?
Yield strength of annealed Al alloy = 150 MPa
Tensile strength of annealed Al alloy = 400 MPa
Yield strength of annealed plain carbon steel = 400 MPa
Tensile strength of annealed plain steel = 700 MPa.
1.9 Describe a specimen preparation procedure for examining:
a. a cross section of a metal needle;
b. a coating layer on metal substrate;
c. lead–tin solder; and
d. polyethylene blended with another crystalline polymer.
1.10 Which parts of a specimen will be highlighted under dark-field illumination
in an optical microscopic study if the specimen is a polycrystalline metal
with a few ceramic particles?
1.11 Why do we rotate the analyzer when examining microstructure with polarized light?
1.12 Why do we say that the Nomarski contrast may not provide a real threedimensional image?
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44
1.13
1.14
1.15
Suggest an imaging mode to examine a titanium specimen containing both
hexagonal close-packed (HCP) and body-centered cubic (BCC) phases, and
justify your suggestion.
Why is fluorescence microscopy more commonly used in biological and
polymer specimens than in metals and ceramics?
Can we examine a metal or a ceramic specimen with confocal microscopy?
References
1. Murphy, D.B. (2001) Fundamentals of
2.
3.
4.
5.
6.
Light Microscopy and Electronic Imaging,
Wiley-Liss, New York.
Vander Voort, G.F. (1984) Metallography
Principles and Practice, McGraw-Hill Book
Co., New York.
Callister, W.J. Jr., (2006) Materials Science
and Engineering: An Introduction, 7th edn,
John Wiley & Sons, Inc., Hoboken.
Swayer, L.C. and Grubb, D.T. (1996)
Polymer Microscopy, Chapman & Hall,
London.
Scheirs, J. (2000) Compositional and
Failure Analysis of Polymers: A Practical Approach, John Wiley & Sons, Ltd,
Chichester.
Müller, M. (2006) Introduction to Confocal Fluorescence Microscopy, 2nd edn,
The International Society for Optical
Engineering, Bellingham, WA.
7. Clarke, A.R. and Eberhardt, C.N. (2002)
Microscopy Techniques for Materials
Science, Woodhead Publishing Ltd,
Cambridge.
Further Reading
Bradbury, S.S. and Bracegirdle, B. (1998)
Introduction to Light Microscopy, BIOS
Scientific Publishers, Oxford.
Rawlins, D.J. (1992) Light Microscopy, BIOS
Scientific Publishers, Oxford.
Hemsley, D.A. (1989) Applied Polymer Light
Microscopy, Elsevier Applied Science,
London.
American Society for Metals (1986) Metals
Handbook, 9th edn, Vol. 10, American
Society for Metals, Metals Park, OH.
45
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Further Reading
2
X-Ray Diffraction Methods
X-ray diffraction methods are the most effective methods for determining the crystal
structure of materials. Diffraction methods can identify chemical compounds from
their crystalline structure, not from their compositions of chemical elements. This
means that the different compounds (or phases) that have the same composition
can be identified. Diffraction methods include X-ray diffraction, electron diffraction,
and neutron diffraction. X-ray diffraction by crystals was discovered in 1912, and
since then it has been the most extensively studied and used technique for
materials characterization. This chapter introduces X-ray diffraction methods. The
theoretical background of diffraction discussed in this chapter is also applied to
other types of diffraction methods. X-ray diffraction methods can be classified into
two types: spectroscopic and photographic. The spectroscopic technique known
as the X-ray powder diffractometry, or simply X-ray diffractometry (XRD), is the
most widely used diffraction method and the main technique discussed in this
chapter. Photographic techniques are not as widely used as diffractometry in
modern laboratories. One reason is that spectroscopic methods can replace most
photographic methods. One of photographic method for wide-angle diffiraction is
introduced even though the spectroscopic method is the focus of this chapter.
2.1
X-Ray Radiation
2.1.1
Generation of X-Rays
X-rays are short-wavelength and high-energy beams of electromagnetic radiation.
X-ray energy is characterized either by wavelength or photon energy. X-rays are
produced by high-speed electrons accelerated by a high-voltage field colliding with
a metal target. Rapid deceleration of electrons on the target enables the kinetic
energy of electrons to be converted to the energy of X-ray radiation. The wavelength
of X-ray radiation (λ) is related to the acceleration voltage of electrons (V) as shown
in the following equation:
λ=
1.2398 × 103
(nm)
V
(2.1)
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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47
2 X-Ray Diffraction Methods
High voltage
Target
Filament
Cooling
Electrons
X-rays
High vacuum
Figure 2.1 X-ray tube structure. X-ray radiation from the anode is guided by the windows
of the tube to produce an X-ray beam for diffraction.
To generate X-rays, we need a device called an X-ray tube. Figure 2.1 illustrates
the structure of an X-ray tube containing a source of electrons and two metal
electrodes in a vacuum tube. The high voltage maintained across these electrodes
rapidly draws the electrons to the anode (target). X-rays are produced at the point
of impact on the target surface and radiated in all directions. There are windows
to guide X-rays out of the tube. Extensive cooling is necessary for the X-ray tube
because most of the kinetic energy of electrons is converted into heat; less than 1%
is transformed into X-rays.
The X-ray tube generates the X-ray radiation with a range of wavelengths
starting from a minimum λ, called continuous X-rays or white X-rays, shown as
the background of radiation spectrum in Figure 2.2. The minimum λ (with the
maximum radiation energy) of continuous X-rays is determined by the maximum
acceleration voltage of electrons in the X-ray tube according to Eq. (2.1). For
example, the minimum λ is 0.062 nm at an acceleration voltage of 20 kV. Figure 2.2
shows that there are sharp intensity maxima at certain wavelengths superimposed
on a continuous X-ray spectrum. These intensity maxima are the characteristic Xrays. X-ray diffraction methods commonly require a source with single-wavelength
(monochromatic) X-ray radiation. The monochromatic radiation must come from
the characteristic X-rays that are generated by filtering out other radiations from
the spectrum.
The physical principles of characteristic X-ray generation are schematically
illustrated in Figure 2.3. When an incident electron has sufficient energy to excite
an electron in the inner shell of an atom to a higher-energy state, the vacancy left
in the inner shell will be filled by an electron in an outer shell. As the electron
falls to the inner shell, energy will be released by emitting an X-ray with a specific
wavelength or photons with specific energy.
For example, a K-shell vacancy can be filled by an electron from either the L shell
or M shell, which results in emitting the characteristic K α or Kβ X-rays, respectively
(Figure 2.2). Similarly, when a vacancy in the L shell is filled by an electron of the
M shell, the Lα X-rays will be emitted. The probability of an L shell electron filling
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48
6
X-ray intensity (relative units)
5
Kα
Characteristic
radiation
4
Continuous
radiation
25 kV
3
Kβ
20
2
15
1
10
SWL
0
5
1.0
0
2.0
3.0
Wavelength (angstroms)
Figure 2.2 X-ray spectra generated with a molybdenum target at various acceleration voltages. The continuous X-rays have a short wavelength limit (SWL). Characteristic radiations
exhibit single wavelengths of high intensity superimposed on the continuous radiation background. (Reproduced with permission from [1].)
L3
L2
L1
Kβ
Kα
K
L
M
Kα1
Kα2
K
Nucleus
Figure 2.3 Schematic illustration of characteristic X-ray radiation.
the K shell vacancy is much higher than that of an M shell electron. Thus, the
intensity of Kα X-rays is higher than that of Kβ. More precisely, Kα contains two
characteristic lines: Kα 1 and Kα 2 , with the latter wavelength being slightly longer
than the former. This phenomenon results from the subshell structure of the L
shell as indicated by L1 and L2 and L3 . Kα 1 is the radiation when electrons fall
from the L3 to K shell; Kα 2 is generated when electrons fall from the L2 to K shell
(Figure 2.3).
Kα 1 , Kα 2 , and Kβ are the three strongest characteristic X-rays are used for
diffraction radiation. The wavelength differences between Kα 1 and Kα 2 are so small
that they are not always resolved as separate radiation. For example, wavelengths
49
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2.1 X-Ray Radiation
2 X-Ray Diffraction Methods
Table 2.1
Characteristic X-rays of anode materials.
Anode
Material
Atomic
Number
Kα (nm)
Critical excitation
Potential (keV)
Optimum
Voltage (kV)
24
26
29
42
0.22291
0.1937
0.1542
0.0710
5.99
7.11
8.98
20.00
40
40
45
80
Cr
Fe
Cu
Mo
generated by a copper target are approximately the following.
λKα1 = 0.15406 nm
λKα2 = 0.15444 nm
λKβ = 0.13922 nm
We often simply call Kα 1 and Kα 2 radiations the Kα doublet. The K α doublet is the
most widely used monochromatic X-ray source for diffraction work. Table 2.1 lists
the commonly used Kα doublets, of which the wavelength is an average of Kα 1
and Kα 2 .
2.1.2
X-Ray Absorption
To obtain monochromatic Kα, a filter system is necessary to filter out the continuous
X-rays and other characteristic X-rays, which are not generated with Kα from the
X-ray tube. X-ray filters can be made from material that strongly absorbs X-rays
other than Kα. Generally, materials exhibit various abilities to absorb X-rays. X-ray
absorption by materials is a function of the linear absorption coefficient (μ) and
mass density (ρ). The X-ray intensity (I) passing through an absorption layer with
thickness x is expressed by the following equation.
Ix = Io e(μ/ρ)ρx
(2.2)
Equation (2.2) expresses the exponential in terms of (μ/ρ), which is called the
mass absorption coefficient. It is independent of the physical state of the solid or
liquid. The mass absorption coefficient varies with chemical element; an element
of higher atomic number has a higher μ/ρ value than an element of lower atomic
number.
The mass absorption coefficient generally decreases with decreasing wavelength
of X-ray radiation. For example, Figure 2.4 shows the change in μ/ρ of barium
in a wavelength range of X-ray radiation. Figure 2.4 also shows that the μ/ρ
curve sharply jumps at certain wavelengths, marked as LIII , LII , LI , and K. A
jump-up point in the curve is called the absorption edge of the mass absorption
coefficient. The reason μ/ρ increases sharply at certain wavelengths is that energies
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50
Mass absorption coefficient
300
LI
LII
LIII
200
100
K
0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
λ [Å]
Figure 2.4 X-ray absorption curve of barium. (Reproduced with permission from Ref. [2].)
of X-ray radiation, represented by the wavelengths, are sufficient to excite certain
characteristic X-ray radiations in barium. The absorption edges of LIII , LII , LI , and
K represent the excitation of LIII , LII , LI , and K characteristic X-rays in barium,
respectively.
The feature of the absorption edge can be used for X-ray radiation filtering. The
X-ray filtering mechanism is illustrated in Figure 2.5. We may select a filter material
of which the absorption edge is located at a wavelength slightly shorter than that of
Kα radiation. The filter material can effectively absorb Kβ and continuous X-rays
with wavelengths shorter than the absorption edge, as shown in Figure 2.5.
X-ray intensity
mass absorption coefficient
Kα
Kα
Kβ
Kβ
1.2
1.4
1.6
λ (angstroms)
(a) No filter
1.8
1.2
1.4
1.6
λ (angstroms)
1.8
(b) Nickel filter
Figure 2.5 Filtering mechanism of X-ray radiation. Spectra of X-ray radiation are compared:
(a) before and (b) after filtering. The dotted line indicates the sharp increase of absorption
at a slightly shorter wavelength than the Kα radiation that enables a nickel filter to generate
single-wavelength radiation. (Reproduced with permission from Ref. [1].)
51
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2.1 X-Ray Radiation
2 X-Ray Diffraction Methods
2.2
Theoretical Background of Diffraction
2.2.1
Diffraction Geometry
2.2.1.1 Bragg’s Law
X-rays are electromagnetic waves, as are visible light, but the X-ray wavelength
is much shorter than visible light, only of the order of 0.1 nm. X-ray diffraction
methods are based on the phenomenon of wave interferences, as introduced in
Section 1.4.2. Two light waves with the same wavelength and traveling in the
same direction can either reinforce or cancel each other, depending on their
phase difference. When they have a phase difference of nλ (n is an integer),
called ‘‘inphase,’’ constructive interference occurs; however, when they have a
phase difference of nλ/2, called ‘‘completely out of phase,’’ completely destructive
interference occurs, as illustrated in Figure 2.31.
X-ray beams incident on a crystalline solid will be diffracted by the crystallographic
planes as illustrated in Figure 2.6. Two inphase incident waves, beam 1 and beam
2, are deflected by two crystal planes (A and B). The deflected waves will not be
inphase except when the following relationship is satisfied.
nλ = 2d sin θ
(2.3)
Equation (2.3) is the basic law of diffraction called Bragg’s Law. Bragg’s Law can
be simply obtained by calculating the path differences between the two beams in
Figure 2.6. The path difference depends on the incident angle (θ ) and the spacing
1
Incident
beam
2
A
λ
λ
P
θ
S
θ
θ
θ
1′ Diffracted
beam
2′
A′
dhkl
T
B′
B
Q
Figure 2.6 Bragg diffraction by crystal planes. The path difference between beams 1 and 2
is SQ + QT = 2PQ sinθ . (Reproduced with permission from Ref. [3].)
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52
between the parallel crystal planes (d). In order to keep these beams inphase, their
path difference (SQ + QT = 2d sin θ ) has to equal one or multiple X-ray wavelengths
(nλ).
We are able to obtain information on the spacing between atomic planes of a
crystal when constructive interference is detected at a given incident angle and a
wavelength of the incident beam, based on Bragg’s Law. Knowing the spacings
of crystallographic planes by diffraction methods, we can determine the crystal
structure of materials. For example, the plane spacing of cubic crystal relates to the
lattice parameter (a) by the following equation.
a
dhkl = √
h2 + k2 + l2
(2.4)
The Miller indices (hkl) represent a series of parallel planes in a crystal with spacing
of dhkl . Combining Eqs. (2.3) and (2.4), we obtain the following relationship between
diffraction data and crystal parameters for a cubic crystal system.
sin2 θ =
λ2 2
(h + k2 + l2 )
4a2
(2.5)
Equation (2.5) does not directly provide the Miller indices of crystallographic planes.
We need to convert (h2 + k2 + l2 ) to (hkl) or {hkl}. This should not be difficult for
low-index planes of cubic systems. For example, when (h2 + k2 + l2 ) is equal to 1,
the plane index must be {001}; when it is equal to 2, the index must be {110}.
This type of calculation is often not necessary because the relationship between
deflection angle and the Miller indices of most crystalline materials, for a given λ,
have been determined and published by the International Centre for Diffraction
Data (ICDD).
2.2.1.2 Reciprocal Lattice
A crystallographic plane (hkl) is represented as a light spot of constructive interference when the Bragg conditions (Eq. (2.3)) are satisfied. Such diffraction spots
of various crystallographic planes in a crystal form a three-dimensional array that
is the reciprocal lattice of the crystal. The reciprocal lattice is particularly useful
for understanding a diffraction pattern of crystalline solids. Figure 2.7 shows a
plane of a reciprocal lattice in which an individual spot (a lattice point) represents
crystallographic planes with Miller indices (hkl).
A reciprocal lattice is in an imaginary reciprocal space that relates to the
corresponding crystal lattice in real space. A direction in the crystal lattice is
defined by a vector ruvw with unit vectors a, b, and c in real space
ruvw = ua + vb + wc
(2.6)
where u, v, and w are integers for indexing crystallographic directions. Similarly,
we can define a direction in reciprocal lattice by a vector d ∗hkl with the reciprocal
unit vectors a* , b* , and c* in reciprocal space.
d ∗hkl = ha∗ + kb∗ + lc∗
(2.7)
53
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2.2 Theoretical Background of Diffraction
2 X-Ray Diffraction Methods
b∗
530
030
130 230 330
430 530
020
120 220 320
420 520
010
110 210 310
410 510
100 200 300
400 500
a∗
a∗
500
030
530
530
b∗
Figure 2.7 A reciprocal lattice plane of a simple tetragonal crystal. The indices of lattice
points are those of the crystallographic plane that the points represent. (Reproduced with
permission from Ref. [2])
A dimension in reciprocal space is a reciprocal of the dimension in real space (with
a factor of unity). The magnitude of a vector d ∗hkl in a reciprocal lattice equals the
reciprocal of plane spacing (dhkl ) in real space.
1 ∗
(2.8)
|d hkl | = d hkl The relationship between a reciprocal lattice and its real crystal structure is
highlighted as follows:
• A crystal structure always has a unique reciprocal lattice structure (as defined by
Eqs. (2.7) and (2.8)).
• Each lattice point in reciprocal space represents a crystal plane (hkl). The direction
of d ∗hkl is perpendicular to the crystal plane (hkl).
• The relationship between the unit vectors of true and reciprocal lattices should
be
a∗ ⊥b and c, b∗ ⊥c and a, c∗ ⊥a and b, aa∗ = bb∗ = cc∗ = 1.
• It is not generally true that a* //a, b* //b, and c* //c unless the crystal is orthogonal
(a ⊥ b, b ⊥ c and c ⊥ a). For example, Figure 2.8 shows an example where a* is
perpendicular to the (100) plane and a is parallel to the [100] directions. The [100]
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54
c
c∗
a∗
b∗
b
a
Figure 2.8 Relationship between directions of unit vectors in a real crystal lattice (a, b,
c) and its reciprocal lattice (a* , b* , c* ).a* must be perpendicular to b and c because a*
is perpendicular to the (100) plane. Generally, a* is not parallel to a, except in orthogonal
systems.
directions in real space are not perpendicular to the (100) planes if [100] are not
perpendicular to [010] and [001].
• Crystal planes belonging to one crystal zone (a group of crystallographic planes
of which the normal directions are perpendicular to one direction called the
zone axis direction) form one reciprocal lattice plane. The zone axis direction
is perpendicular to that reciprocal lattice plane. For example, Figure 2.9 shows
an example of the relationship between crystal zone [001] and the reciprocal
lattice plane. The reciprocal lattice plane is composed of the diffraction spots of
crystallographic planes belonging to the [001] zone.
2.2.1.3 Ewald Sphere
Bragg’s Law describes the necessary conditions to detect crystal planes by diffraction. The conditions can also be graphically expressed by the Ewald sphere method
using the concept of the reciprocal lattice. Figure 2.10 illustrates the construction
of the Ewald sphere. The Ewald sphere is an imaginary sphere with a radius of
λ− 1 in reciprocal space. The center of the Ewald sphere is located at a crystal to be
examined. The incident beam is represented by a line that passes through a crystal
at the sphere center and targets the origin of the reciprocal lattice located on the
surface of the sphere (CO). The diffraction beam is represented by line connect the
55
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2.2 Theoretical Background of Diffraction
2 X-Ray Diffraction Methods
[001]
(100)
Diffraction planes
(010)
(110)
Beam
Diffraction pattern
010
110
110
100
110
100
110
010
Figure 2.9 Relationship between a reciprocal lattice plane and real space directions. The
reciprocal lattice plane is composed of diffraction spots from crystal planes (hk0). The zone
axis [001] is perpendicular to the reciprocal lattice plane.
a∗
b∗
B
080
d ∗(230)
300
A
X-ray
Beam
C
2θ
Crystal
030
b∗
Figure 2.10 Construction of the Ewald sphere. The Bragg conditions for plane (230) are
satisfied when its reciprocal lattice point touches the surface of the Ewald sphere. (Reproduced with permission from Ref. [2].)
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56
sphere center and a lattice point of the reciprocal lattice (CB). The angle between
lines CO and CB should be twice that of θ defined in Figure 2.6. Changing the
diffraction angle (2θ ) can be represented by rotation of the reciprocal lattice around
its origin, point O in Figure 2.10. The Bragg conditions are satisfied when a lattice
point touches the Ewald sphere surface. It can be proved that these geometric
relationships represented in the Ewald sphere are equivalent to Bragg’s Law, using
Figure 2.10 as an example.
d∗
1
, OA = 230
λ
2
∗
/2
d230
OA
=
Hence, sin θ =
OC
1/λ
1
Recall d230 = ∗
d230
Since OC =
Thus, λ = 2d230 sin θ.
This equivalence allows us to detect diffraction from crystallographic planes when the
corresponding reciprocal lattice points touch the Ewald sphere surface. Formation of
diffraction patterns from a single crystal can be well illustrated by the Ewald sphere, as
shown in Figure 2.11, which is commonly seen by electron diffraction in a transmission
electron microscope (TEM). The electron wavelength in TEM is even shorter than X-rays
(∼0.0037 nm with acceleration voltage of 100 kV). For an incident beam with such a
short wavelength (λ), the radius of the Ewald sphere (λ− 1 ) is huge (∼100 times larger
than the value of d * for a low Miller index plane). Thus, the surface of the Ewald sphere
is flat compared with the unit vectors of the reciprocal lattice for crystals. The relatively
Ewald sphere
Figure 2.11 Formation of a single-crystal
diffraction pattern in transmission electron
microscopy. The short wavelength of electrons makes the Ewald sphere flat. Thus,
the array of reciprocal lattice points in a
reciprocal plane touches the sphere surface
and generates a diffraction pattern on the
TEM screen. The outer ring may be visible
when the Ewald sphere surface touches the
reciprocal plane above the original plane.
57
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2.2 Theoretical Background of Diffraction
2 X-Ray Diffraction Methods
flat surface of the Ewald sphere touches a number of reciprocal lattice points, and these
points form a diffraction pattern on the screen of a TEM, as shown in the lower part of
Figure 2.11.
The Ewald sphere also predicts a ring-type diffraction pattern in a polycrystalline
material, which is considered as an aggregate of the crystals with all possible orientations in three-dimensional space. We may consider that placing a polycrystalline
solid at the center of the Ewald sphere is equivalent to the case of a single crystal by
rotating the reciprocal lattice around its origin in all directions of reciprocal space.
Rotation of a reciprocal lattice in all directions reveals all possible crystallographic
planes satisfying the Bragg conditions. Figure 2.12 illustrates the diffraction pattern
of a polycrystalline solid recorded by the method of powder X-ray photography. The
polycrystalline diffraction patterns shown at the right-hand side of Figure 2.12 are
called the Debye rings recorded on a negative film with a central hole.
2.2.2
Diffraction Intensity
In the previous section, we were only concerned with diffraction conditions stated
in Bragg’s Law. Satisfying such conditions does not guarantee that we can detect or
see diffraction from crystallographic planes because there is an issue of diffraction
intensity. Diffraction intensity may vary among planes even though the Bragg conditions are satisfied. This section does not extensively discuss diffraction intensity,
but only introduces important factors affecting the intensity of the X-ray diffraction.
EWALD
sphere
incident
X-ray beam
Powder
specimen
∗
e.g. d 100
Diffracted
rays
‘‘DEBYE RING’’
of diffraction
Figure 2.12 The Ewald sphere method illustrates the ring pattern of diffraction from a
powder specimen. The Debye ring recorded
by the Hull–Debye–Scherrer method results from randomly oriented crystals in
the powder specimen, in which reciprocal
lattice points of (hkl) touch the Ewald sphere
surface in various directions to form individual rings. It is equivalent to rotating a
reciprocal lattice along an incident beam
axis. (Reproduced with permission from
Ref. [2].)
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58
59
X-ray diffraction by a crystal arises from X-ray scattering by individual atoms in
the crystal. The diffraction intensity relies on collective scattering by all the atoms
in the crystal. In an atom, the X-ray is scattered by electrons, not the nucleus of the
atom. An electron scatters the incident X-ray beam to all directions in space. The
scattering intensity is a function of the angle between the incident beam and the
scattering direction (2θ ). The X-ray intensity of electron scattering can be calculated
by the following equation
I(2θ ) =
Io 1 + cos2 (2θ )
K
r2
2
(2.9)
Io is the intensity of the incident beam, r is the distance from the electron to
the detector, and K is a constant related to atom properties. The last term in the
equation shows the angular effect on intensity, called the polarization factor. The
incident X-ray is unpolarized, but the scattering process polarizes it.
The total scattering intensity of an atom at a certain scattering angle, however,
is less than the simple sum of intensities of all electrons in the atom. There is
destructive interference between electrons due to their location differences around
a nucleus, as illustrated in Figure 2.13a. Destructive interference that results from
the path difference between X-ray beams scattered by electrons in different locations
is illustrated in Figure 2.13b. Figure 2.13b shows an example of a copper atom,
which has 29 electrons. The intensity from a Cu atom does not equal 29 times that
of a single electron in Eq. (2.9) when the scattering angle is not zero. The atomic
(b) 30
29
(a)
X
Z
A
D
20
Z′
fCu
X′
C
10
B
Y
Y′
0
0
0.2
0.4
0.6
sin θ
−1
λ (Å )
Figure 2.13 (a) Scattering of an X-ray by electrons in an atom and (b) the intensity of a
scattered beam represented by the atomic scattering factor (f ), which is a function of scattering angle (θ ) with the maximum value at 0◦ . The maximum is equal to the number of
electrons in the atom. (Reproduced with permission from Ref. [1, 2].)
0.8
1.0
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2.2 Theoretical Background of Diffraction
2 X-Ray Diffraction Methods
scattering factor (f ) is used to quantify the scattering intensity of an atom.
f =
amplitude of the wave scattered by one atom
amplitude of the wave scatter by one electron
(2.10)
The atomic scattering factor is a function of scattering direction and X-ray wavelength, as shown in Figure 2.13b for copper atom. The scattering intensity of an
atom is significantly reduced with increasing 2θ when the X-ray wavelength is
fixed.
2.2.2.1 Structure Extinction
The most important aspect of intensity calculations is the structure extinction. This
term refers to interference between scattering atoms in a unit cell of a crystal. If
there is more than one atom in a unit cell (for example, a face-centered cubic (FCC)
lattice has four atoms in a unit cell), intensity from certain crystallographic planes
can become extinct due to interference between atoms on different planes. Figure
2.14 illustrates this concept by comparing diffraction from two unit cells that have
the same size. When the Bragg conditions are satisfied for (001) plane diffraction,
and thus, the path difference ABC equals one wavelength, diffraction from the (001)
plane of the base-centered crystal (Figure 2.14a) can be seen. However, diffraction
from the (001) plane of a body-centered crystal cannot be seen because the path
difference DEF between rays 1 and 3 is exactly equal to half that of the rays
1 and 2 , ABC, or one-half wavelength (Figure 2.14b). Thus, rays 1 and 3 are
completely out of phase and annul each other. Similarly, ray 2 will be annulled
by the plane below it. This means that no diffraction from the (001) plane in a
c
b
a
(a)
1
(b)
1
1′
θ
θ
3
1′
2
2
θ
θ
D
F
2′
2′
c
3′
E
C
A
B
C
A
B
a
Figure 2.14 Structure extinction: (a) no structure extinction in the (001) planes in a facecentered crystal structure and (b) structure extinction in the (001) planes of body-centered
crystal structure in which Bragg diffraction of beams 1 and 2 is canceled out by beam 3
from the plane of the body center. (Reproduced with permission from Ref. [1].)
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60
body-centered crystal can be detected. Note that diffraction of a (002) plane in a
body-centered crystal can be detected at another θ angle that it makes DEF equal to
one wavelength.
The structure extinction of intensity can be calculated by the structure factor (F).
Suppose that there are N atoms per unit cell, and the location of atom n is known
as un , vn , wn, and its atomic structure factor is f n . The structure factor for the (hkl)
plane (Fhkl ) can be calculated.
Fhkl =
N
fn exp[2πi(hun + kvn + lwn )]
(2.11)
n
For example, a body-centered cubic (BCC) unit cell has two atoms located at [0,0,0]
and [0.5,0.5,0.5]. We can calculate the diffraction intensity of (001) and (002) using
Eq. (2.11).
F001 = f exp[2πi(0 + 0 + 1 × 0) + f exp[2πi(0 × 0.5 + 0 × 0.5 + 1 × 0.5)]
= f + f exp[πi] = 0
F002 = f exp[2πi(0 + 0 + 2 × 0) + f exp[2πi(0 × 0.5 + 0 × 0.5 + 2 × 0.5)]
= f + f exp[2πi] = 2f
This structure-factor calculation confirms the geometric argument of (001) extinction in a body-centered crystal. Practically, we do not have to calculate the structure
extinction using Eq. (2.11) for simple crystal structures such as BCC and FCC.
Their structure extinction rules are given in Table 2.2, which tells us the detectable
crystallographic planes for BCC and FCC crystals. From the lowest Miller indices,
the planes are given as following.
BCC(1 1 0), (2 0 0), (2 1 1), (2 2 0), (3 1 0), (2 2 2), ( 3 2 1), . . .
FCC(1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2), (3 3 1), . . .
For a unit cell with more than one type of atom, the calculation based on Eq. (2.11)
will be more complicated because the atomic scattering factor varies with atom
type. We need to know the exact values of f for each type of atom in order to
calculate F. Often, reduction of diffraction intensity for certain planes, but not total
extinction, is seen in crystals containing multiple chemical elements.
Table 2.2
Structure extinction rules for crystallographic plane (hkl).
Lattice type
Diffraction possibly present
Diffraction necessarily absent
Simple
Base-centered
Base-centered
Face-centered
All
h and k unmixeda
(h + k + l) even
h, k, and l unmixed
None
h and k mixeda
(h + k + l) odd
h, k, and l mixed
a
Applies to a cell with (00 l) face centered.
61
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2.2 Theoretical Background of Diffraction
2 X-Ray Diffraction Methods
2.3
X-Ray Diffractometry
XRD, the most widely used X-ray diffraction technique in materials characterization,
was originally used for examining the crystal structure of powder samples; thus,
traditionally it is called X-ray powder diffractometry. In fact, polycrystalline aggregate
solids other than powder are commonly examined by this technique. The XRD
instrument is called an X-ray diffractometer. In the diffractometer, an X-ray beam of
a single wavelength is used to examine polycrystalline specimens. By continuously
changing the incident angle of the X-ray beam, a spectrum of diffraction intensity
versus the angle between incident and diffraction beam is recorded. Diffractometry
enables us to identify the crystal structure and quality by analyzing then comparing
the spectrum with a database containing over 60 000 diffraction spectra of known
crystalline substances.
2.3.1
Instrumentation
The basic function of a diffractometer is to detect X-ray diffraction from materials
and to record the diffraction intensity in a range of the diffraction angle (2θ ). Figure
2.15 demonstrates the geometrical arrangement of the X-ray source, specimen, and
detector. The X-ray radiation generated by an X-ray tube passes through special
slits that collimate the X-ray beam. These Soller slits are commonly used in the
diffractometer. They are made from a set of closely spaced thin metal plates parallel
to the figure plane of Figure 2.15 to prevent beam divergence in the direction
perpendicular to the figure plane. A divergent X-ray beam passing through the slits
Detector
Receiving slit Soller
slit
Monochromator
2θ
Antiscatter slit
X-ray tube
(line focus)
Soller slits
θ
Sample
Divergence slit
Measuring circle
Figure 2.15
Geometric arrangement of X-ray diffractometer.
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62
strikes the specimen. The specimen is usually in the form of a flat plate that is
supported by a specimen table (not shown in Figure 2.15). X-rays are diffracted by
the specimen and form a convergent beam at the receiving slits (RSs) before they
enter a detector.
The diffracted X-ray beam needs to pass through a monochromatic filter (or a
monochromator) before being received by a detector. Commonly, the monochromatic filter is placed in the diffracted beam path instead of the incident beam
path. This arrangement can suppress wavelengths other than Kα radiation and
also decrease the background radiation originating within the specimen. Modern
diffractometers commonly use a monochromator made from a graphite crystal that
is designed to diffract a single wavelength based on Bragg’s Law.
Relative movements among the X-ray tube, specimen, and the detector ensure
the recording of diffraction intensity in a range of 2θ . Note that the θ angle is not
the angle between the incident beam and specimen surface; rather it is the angle
between the incident beam and the crystallographic plane that generates diffraction.
Diffractometers can have various types of geometric arrangements to enable
collection of X-ray data. The majority of commercially available diffractometers use
the Bragg–Brentano arrangement, in which the X-ray incident beam is fixed, but a
sample stage (not shown in Figure 2.15) rotates around the axis perpendicular to
the figure plane of Figure 2.15 in order to change the incident angle. The detector
also rotates around the axis perpendicular to the plane of the figure but its angular
speed is twice that of the sample stage in order to maintain the angular correlation
of θ − 2θ between the sample and detector rotation.
The Bragg–Brentano arrangement, however, is not suitable for thin samples
such as thin films and coating layers. The technique of thin-film XRD uses a special
optical arrangement for detecting the crystal structure of thin films and coatings on
a substrate. The incident beam is directed to the specimen at a small glancing angle
(usually < 1◦ ) and the glancing angle is fixed during operation and only the detector
rotates to obtain the diffraction signals, as illustrated in Figure 2.16. Thin-film XRD
requires a parallel incident beam, not a divergent beam as in regular diffractometry.
Also, a monochromator is placed in the optical path between the X-ray tube and the
specimen, not between the specimen and the detector. The small glancing angle of
the incident beam ensures that sufficient diffraction signals come from a thin film
or a coating layer instead of the substrate.
Detector
X-ray
Collimator
<1°
Figure 2.16 Optical arrangement for thin-film diffractometry.
63
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2.3 X-Ray Diffractometry
2 X-Ray Diffraction Methods
2.3.1.1 System Aberrations
In ideal conditions, an X-ray beam focuses on a specimen and the intensity of
diffraction from the specimen is detected accurately at the 2θ angle. The focusing
arrangement in a diffractometer, however, cannot ensure true focusing due to
features of the X-ray source and specimen. Thus, errors due to parafocusing always
exist. The errors of parafocusing are referred to as:
• axial divergence error;
• flat-specimen error; and
• specimen-transparency error.
Errors due to parafocusing can be illustrated using the Bragg–Brentano arrangement of the diffractometer as shown in Figure 2.17. The X-ray source is fixed at
F, but the RS coupled with the detector rotates along the axis perpendicular to the
plane of the figure on a circle centered at the specimen surface with radius R (the
goniometer circle). The surface of the specimen rotates along the same axis at half
the rotation speed of RS, remaining tangential to a focusing circle with radius of r f .
This arrangement of rotations ensures the scan over a range of 2θ angles. As shown
in Figure 2.17, the incident X-ray beam has a certain degree of divergence; part of
the specimen surface is not located on the focusing circle and the atomic planes
inside the specimen are not located on the focusing circle. These aforementioned
conditions generate system errors that affect the peak positions and widths in the
diffraction spectrum.
Besides conventional XRD, high-resolution X-ray diffractometry (HRXRD) was developed in recent years. HRXRD is mainly used for examining the crystal quality of thin
films and epitaxial layers on single-crystal substrates. The main features of the HRXRD
instrument are that highly monochromatic X-rays are used (only K α 1 , not K α 2 ) and the
specimen stage is able to rotate with three degrees of freedom. Such features enable us
rf
F
RS
S
Θ
20
R
Figure 2.17 System aberrations of the X-ray diffractometer due to axial-divergence and flatspecimen errors. (Reproduced with permission from Ref. [2].)
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64
to obtain highly accurate information including crystal orientation of a thin film with
respect to its substrate, lattice mismatch of an epitaxial layer, and elastic strain in thin
coatings.
2.3.2
Samples and Data Acquisition
2.3.2.1 Sample Preparation
The X-ray diffractometer was originally designed for examining powder samples.
However, the diffractometer is often used for examining samples of crystalline
aggregates other than powder. Polycrystalline solid samples and even liquids can
be examined. Importantly, a sample should contain a large number of tiny crystals
(or grains) which randomly orient in three-dimensional space because standard
X-ray diffraction data are obtained from powder samples of perfectly random
orientation. Relative intensities among diffraction peaks of a nonpowder sample
can be different from the standard because perfect randomness of grain orientation
in solid samples is rare. The best sample-preparation methods are those that allow
analysts to obtain the desired information with the least amount of treatment
because chemical contamination may occur during the sample treatments.
Another sample-related issue is that X-ray penetration into matter is limited
because of X-ray absorption in matter. A certain depth from the surface can only
be examined. Table 2.3 lists typical penetration depths for three types of materials.
Obviously, X-rays penetrate deeper in materials composed of lighter elements than
those of heavy elements.
2.3.2.2 Acquisition and Treatment of Diffraction Data
A diffractometer records changes of diffraction intensity with 2θ . The diffractometer
records the diffraction intensity starting from a low 2θ and ending at a high 2θ .
Figure 2.18 shows the X-ray diffraction spectrum for a powder mixture of Si and
Al2 O3 . A number of intensity peaks located at different 2θ provide a ‘‘fingerprint’’
for a crystalline solid such as Al2 O3 . Each peak represents diffraction from a certain
crystallographic plane. Matching an obtained peak spectrum with a standard
spectrum enables us to identify the crystalline substances in a specimen.
Table 2.3
Penetration depths of Cu Kα radiation with different incident angles.
Material
μ
ρ
MoO3
CaCO3
Aspirin
92.7
39.9
7.0
ρ (g cm − 3 )
20◦ (μm)
40◦ (μm)
60◦ (μm)
4.71
2.71
1.40
1.8
7.4
82
2.7
11
121
3.6
15
161
Data taken from Ref. [2] © 1996 John Wiley & Sons Inc.
65
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2.3 X-Ray Diffractometry
Al2O3
25
30
35
40
45
50
2θ (degree)
55
214
300
400
311
116
110
024
113
104
220
Si
012
Relative intensity
111
2 X-Ray Diffraction Methods
60
65
70
Figure 2.18 The experimental diffraction pattern of a silicon and Al2 O3 mixture. Numbers
with three digits mark the Miller indices of corresponding crystallographic planes.
Table 2.4
Radiation
CrKα
CoKα
CuKα
MoKα
Maximum and minimum measurable plane spacing with characteristic radiation.
Wavelength
(nm)
Maximum
d (nm)
Minimum
d (nm)
0.2291
0.1790
0.1542
0.0709
6.56
5.13
4.42
2.03
0.116
0.091
0.078
0.036
Spectrum matching is determined by the positions of the diffraction peak maxima
and the relative peak intensities among diffraction peaks.
In a modern diffractometer, data acquisition and treatment are mainly done
by computer. To obtain adequate and data of sufficient quality for identifying a
material, the following factors are important:
• Choice of 2θ range: commonly a range of about 5–65◦ is necessary with an
unknown material.
• Choice of X-ray radiation: copper Kα is the most popular radiation source used
in diffractometry because of its short wavelength. Table 2.4 lists the detection
limitations of X-ray radiations commonly used in diffractometry.
• Choice of step width for scanning: scanning in a 2θ range is not continuous, but
in progressive steps. Choosing the step width is a trade-off between accuracy in
peak location and peak intensity. While it might seem that scanning in narrow
steps would be more accurate, in fact small step widths may lead to peak shifts.
On the other hand, a large step width may lead to suppression of peak intensity.
The rule of thumb is to use about 10–20 individual data points above the full
width at half-maximum (FWHM) as B marked in Figure 2.19. For example, for a
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66
(a)
1I
2 max
B
2θ2 2θB 2θ1
2θ
Intensity
Intensity
Imax
2θB
(b)
2θ
Figure 2.19 Comparison of: (a) a real diffraction peak and (b) an ideal peak in a spectrum. B marks the full width at half-maximum intensity (FWHM). (Reproduced with permission from Ref. [1].)
typical peak that has a width of about 0.1–0.3◦ in 2θ , a step width of 0.02◦ in 2θ
is reasonable.
To obtain a satisfactory diffraction spectrum, the following treatments of diffraction data treatment should be done:
• smooth the spectrum curve and subtracting the spectrum background;
• locate peak positions; and
• strip Kα 2 from the spectrum, particularly for peaks in the mid-value range of 2θ .
Recorded diffraction peaks always have a finite width and are not single lines, as
illustrated in Figure 2.19. The location of a peak position can be determined as the
point of a peak curve where the first derivative equals zero. To ensure the accuracy
of a peak position, an external standard made by a suitable material with known
peak positions should be used to calibrate the acquired 2θ value. Comparing known
peak positions of the standard with peaks acquired in the diffractometer, we can
detect system errors (2θ ) of the diffractometer. The 2θ error against a 2θ range
should be corrected before analyzing a spectrum of sample to be examined.
2.3.3
Distortions of Diffraction Spectra
2.3.3.1 Preferential Orientation
A diffraction spectrum is considered a ‘‘fingerprint’’ for identifying examined
materials. An acquired spectrum should be compared with the standard from an
X-ray diffraction database. The standard spectrum has been collected from a pure
powder sample with fine powder size, usually several micrometers in diameter. We
would expect to match both peak locations and relative peak intensities between
the acquired spectrum and the standard if the sample is the same substance as the
67
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2.3 X-Ray Diffractometry
2 X-Ray Diffraction Methods
standard. Matching relative intensities, however, is not always possible even when
the examined specimen has the same crystalline structure as the standard. One
reason for this discrepancy might be the existence of preferential crystal orientation
in the sample. This often happens when we examine coarse powder or nonpowder
samples. The preferential orientation of crystals (grains in solid) may even make
certain peaks invisible.
2.3.3.2 Crystallite Size
Ideally, a Bragg diffraction peak is a line without width, as shown in Figure 2.19b.
In reality, diffraction from a crystal specimen produces a peak with a certain width,
as shown in Figure 2.19a. The peak width can result from instrumental factors
and the size effect of the crystals. Small crystals cause the peak to be widened due
to incompletely destructive interference. This phenomenon can be understood by
examining the case illustrated in Figure 2.20.
A diffraction peak is generated at the Bragg angle θ B satisfying the Bragg
conditions. In a diffractometer, however, the incident X-ray beam is not perfectly
parallel, and the beam includes a range of incident angles from θ 1 to θ 2 which
deviate slightly from θ B . θ 1 and θ 2 should not generate completely constructive
A
A′
B
B′
C
D
C′
D′
θ1
θ2 θ
B
0
d
θB
1
2
t = md
3
M
L
N
m
M′
L′
N′
θB
Figure 2.20 The effect of crystal size on
diffraction peak width can be explained by
incomplete destructive interference at angles
that slightly deviate from the Bragg angle.
For example, the completed destructive interference at angle θ 1 relies on the path
difference between B and L being exactly a
half-wavelength. However, diffracted beam L
does not exist for a crystal with thickness (t)
less than md. A similar explanation applies
to the situation at angle θ 2 . (Reproduced
with permission from Ref. [1].)
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68
interference as θ B does, but may not generate completely destructive interference
either. We know from Bragg’s Law that completely destructive interference needs
diffraction from two planes producing exactly one-half wavelength difference of
paths. If the paths of rays with angle θ 1 scattered by the first two planes differ only
slightly from an integral number of wavelengths, a plane lying deep within the
crystal can produce the exact path difference of one-half wavelength. In this case,
no diffraction other than θ B should be visible. However, such a plane lying deep
within the crystal may not exist if a crystal is thin in the direction perpendicular
to the plane. Thus, such incompletely destructive interference generated by X-rays
with incident angles θ 1 and θ 2 will produce a certain level of diffraction intensities
around the Bragg angle θ B in the spectrum, and result in widening of the diffraction
peak. Peak width is inversely related to crystal size; that is, peak width increases
with decreasing crystal particle size, as shown in Figure 2.21.
2.3.3.3 Residual Stress
Any factor that changes the lattice parameters of crystalline specimens can also distort their X-ray diffraction spectra. For example, residual stress in solid specimens
may shift the diffraction peak position in a spectrum. Residual stress generates
strain in crystalline materials by stretching or compressing bonds between atoms.
Thus, the spacing of crystallographic planes changes due to residual stress. According to Bragg’s Law, the Bragg angles should either decrease or increase when the
spacing of the crystallographic plane changes. Peak shifts in spectra occur when
there is residual stress in a sample, as illustrated in Figure 2.22. The tensile stress
of increasing the spacing shifts a peak to lower 2θ , while the compression stress
of decreasing the spacing shifts a peak to higher 2θ in the spectrum. In fact, X-ray
diffraction is an effective tool to examine residual stress in solids.
Line breadth [°2θ ]
3.0
2.0
1.0
Instrumental broadening
0
10 20
50 100 200 5001000 2000 5000 10000
Particle dimension [Å]
Figure 2.21 Change of peak line width with crystal size. (Reproduced with permission from
Ref. [2].)
69
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2.3 X-Ray Diffractometry
2 X-Ray Diffraction Methods
Crystal lattice
Diffraction
line
d0
No strain
(a)
Uniform strain
(b)
2θ
Nonuniform strain
(c)
Figure 2.22 Effects of residual stress and strain on diffraction peak position and shape: (a)
no strain; (b) uniform strain; and (c) nonuniform strain. (Reproduced with permission from
Ref. [2].)
2.3.4
Applications
2.3.4.1 Crystal-Phase Identification
Identification of crystalline substance and crystalline phases in a specimen is
achieved by comparing the specimen diffraction spectrum with spectra of known
crystalline substances. X-ray diffraction data from a known substance are recorded
as a powder diffraction file (PDF). Most PDFs are obtained with CuKα radiation.
Standard diffraction data have been published by the ICDD, and they are updated
and expanded from time to time. For one crystalline substance, there may be
more than one file. The most recently updated file is recommended for phase
identification. The early PDFs may contain errors in data obtained experimentally.
More recently published PDFs are either obtained by more accurate experimental
measurements or by theoretical calculation. A specimen to be identified should
be in a powder form for most accurate matching. When we need to identify the
crystal structure of a specimen that cannot be prepared as powder, matches of peak
positions and relative intensities might be less than perfect. In this case, other
information about the specimen such as chemical composition should be used to
make a judgment.
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70
800
Intensity
600
400
200
0
10
20
30
40
50
60
2θ (degree)
Figure 2.23 Diffraction pattern of a powder specimen of hydroxyapatite.
In a modern diffractometer, computer software performs the search–match task.
All PDFs of the ICDD can be stored in computer. A search–match program can
find all the possible matches for a specimen. The software algorithms also can
identify more than one crystalline phase in a specimen. It searches the recorded
pattern with its background, and adds candidate crystalline phases together to
compose, rather than decompose, an observed multiphase pattern.
Figure 2.23 shows the diffraction spectrum of a powder sample of calcium
phosphate. With the assistance of a computer, we can identify the peak positions in
the spectrum and search for a possible match between the spectrum and a PDF data
file. Additional chemical information is often used to help in the search process.
For example, this specimen contents Ca, P, and O. The computer quickly searches
for a compound containing Ca, P, and O. It finds a match between the diffraction
spectrum of a sample with data for hydroxyapatite (Figure 2.24). There are two
important parameters in a standard data file shown
in Figure 2.24: the position of
diffraction (2θ ) and relative intensities of peaks II1 , or int-f in the PDF. I1 is the
peak intensity with the maximum value in a spectrum. The highest int-f value is
999, which should be read as 0.999 in the relative intensity. The PDF may also list
the corresponding d-spacing of peaks, which are the true crystal properties.
Figure 2.25 shows a nearly perfect match between the pattern and diffraction
data of hydroxyapatite. The powder sample shows 35 peak matches in the 2θ range
of 10–60◦ . Generally, the relative intensities of peaks also match well with the
standard. For example, the highest intensity is at the peak of 2θ = 31.77◦ and the
second highest peak at 2θ = 32.90◦ in the acquired spectrum. Both of their 2θ
values and relative intensities match those in the PDF for hydroxyapatite. The
relative intensities of the peaks, however, do not exactly match all those in the PDF.
The matches for lower-intensity peaks between the spectrum and the standard file
are relatively poorer, even though a sample of fine powder was examined.
71
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2.3 X-Ray Diffractometry
2 X-Ray Diffraction Methods
I/Icor: 1.06
Rad: CuKa1
Lambda: 1.54060
Filter:
d-sp: calculated
ICSD #: 026205
Mineral Name
Hydroxylapatite
->
89.53
Molecular Weight 1004.64
Volume[CD]: 529.09
Dx: 3.153 Dm:
Sys: Hexagonal
Lattice: Primitive
S.G.: P63/m (176)
Cell Parameters:
a 9.424 b
c 6.879
α
β
γ
Ca10 (P O4)6 (OH)2
Calcium Hydroxide Phosphate
Ref: Calculated from ICSD using POWD-12++, (1997)
Ref: Sudarsanan, K., Young, R.A., Acta Crystallogr., Sec. B, 25, 1534 (1969)
Fixed slit
intensity
74-0566
Quality. C
CAS Number:
15
0
2θ
10.832
16.842
18.817
21.762
22.858
25.357
25.883
28.131
28.921
31.766
32.195
32.897
34.063
35.455
38.168
39.197
39.791
40.436
40.845
41.986
42.325
43.876
44.362
45.330
46.381
46.694
30
Int-f
h
k
l
170
46
23
65
63
23
357
88
160
999
514
612
210
39
2
50
205
18
4
56
11
45
11
35
7
281
1
1
1
2
1
2
0
1
2
2
1
3
2
3
2
2
1
2
1
1
3
1
4
2
4
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
1
3
2
0
3
0
1
0
0
0
2
0
1
0
0
1
1
2
2
0
1
2
0
2
1
0
2
0
1
3
1
2
3
0
3
1
2
2θ
48.081
48.586
49.490
50.475
51.255
52.075
52.075
53.220
54.484
55.863
56.318
57.314
58.027
58.164
58.295
58.737
59.925
60.404
61.571
61.704
62.982
63.404
63.998
64.165
65.000
66.412
60
45
2 θ
75
Int-f
h
k
l
122
40
313
161
116
117
117
140
10
59
2
37
15
11
10
8
43
32
32
50
79
16
74
93
69
21
1
2
2
3
1
4
3
0
1
3
5
3
5
2
4
3
2
3
2
1
5
5
3
3
5
1
3
3
1
2
4
0
0
0
0
2
0
1
0
0
1
3
4
3
4
2
0
1
0
2
1
4
2
0
3
1
0
2
3
4
4
2
0
3
1
4
2
0
0
1
1
4
2
0
4
3
1
3
2θ
67.359
68.461
68.985
68.193
69.673
70.075
70.517
70.799
71.362
71.596
72.232
72.436
72.947
73.735
74.012
74.916
75.031
75.622
76.085
76.473
77.021
77.174
77.720
77.947
78.179
80.837
Int-f
h
k
l
1
4
2
2
20
4
1
2
4
37
28
17
3
19
38
13
11
45
24
18
50
44
2
9
56
3
2
3
6
1
5
4
6
5
1
4
5
2
3
5
2
2
6
2
3
6
1
5
3
1
2
2
2
1
0
0
1
3
0
0
1
3
2
0
3
2
4
3
0
1
4
1
4
1
0
6
5
2
4
4
0
5
2
0
1
3
5
1
0
5
3
1
3
4
2
5
2
0
4
3
5
1
2
5
Figure 2.24 A powder diffraction file (PDF) of hydroxyapatite. (Reproduced with permission
from the International Centre for Diffraction Data, ICDD.)
Section 2.3.3 described factors that can affect relative intensities of peaks. These
include the preferential orientation of crystal grains, residual stress, and other
crystal defects. Eventually, we must rely on human judgment to make the final
identification. In this case, the matches of relative intensities are very good in
general and no other calcium phosphate PDFs can provide matches as good as
hydroxyapatite. Thus, hydroxyapatite can be positively identified.
2.3.4.2 Quantitative Measurement
Quantitative analysis can be done to determine the relative amounts of compounds
or phases in a sample of compound/phase mixtures. Quantitative analysis of a
diffraction spectrum is based on the following factor. The intensity of the diffraction
peaks of a particular crystalline phase in a phase mixture depends on the weight
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72
800
Intensity
600
400
200
0
10
20
30
40
50
60
2θ (degree)
Figure 2.25 Match between the diffraction pattern and diffraction lines in the
hydroxyapatite PDF.
fraction of the particular phase in the mixture. Thus, we may obtain weight fraction
information by measuring the intensities of peaks assigned to a particular phase.
Generally, we may express the relationship as the following
Ii =
KCi
μm
(2.12)
where the peak intensity of phase i in a mixture is proportional to the phase weight
fraction (Ci ), and inversely proportional to the linear absorption coefficient of the
mixture (μm ). K is a constant related to the experimental conditions including
wavelength, incident angle, and the incident intensity of the X-ray beam. The
relationship between the intensity and weight fraction is not truly linear because
μm itself is a function of Ci .
On the other hand, measurement of peak intensities is not simply a measurement
of peak heights. First, the background should be extracted from the peaks. Secondly,
the integrated intensity should be measured for quantitative analysis. This means
that the total area under a peak should be measured. Three basic types of peaks are
encountered when attempting quantitative phase analysis (Figure 2.26):
1)
Peak height is proportional to peak area. This simplest situation allows
estimation of peak intensity by measuring the peak height.
2) Peak height is not proportional to peak area. This common situation needs
integration of the peak area.
3) Peak area is overlapped by other peaks. This also frequently occurs and
profile-fitting methods have to be used for peak-area measurement.
There are three main methods for quantitative analysis:
1)
2)
3)
external standard method;
internal standard method; and
direct comparison method.
73
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2.3 X-Ray Diffractometry
2 X-Ray Diffraction Methods
(a)
Area = A
H
(c)
(b)
A
A
Θ1 Θp Θ2
Θp
B
B
Θ3
Θp
Θ3
Θ4
Figure 2.26 Three types of peak shapes in X-ray diffraction pattern: (a) peak height proportional to peak area; (b) peak height not proportional to peak area; and (c) peak area
overlapped by other peaks. (Reproduced with permission from Ref. [2].)
The external standard method needs peak intensities of a particular phase in its
pure form. The internal standard method needs a series of standard mixtures in
which the particular phase contents are known. The direct comparison method is
of most interest and is easy to use because it does not have either of these restrictive
requirements; that is, it does not require samples of pure substances or standard
mixtures of known phase content. The principles of the direct comparison method
are introduced as follows:
The direct comparison method enables us to estimate the weight fraction of a
particular phase by comparing peak intensities between phases in a mixture. For
example, we have a mixture of phases α and β. We may rewrite Eq. (2.12) for a
peak intensity of α phase in a mixture
Iα =
K 2 R α Cα
μm
(2.13)
where constant K is divided into K 2 and Rα . K 2 is related to the X-ray source only.
Rα is a parameter related to the diffraction angle and crystal properties of phase,
which can be evaluated using the following equation
1 + cos2 2θ
1
2
(e−2M )
(2.14)
|Fhkl | p
R=
v2
sin2 θ cos θ
R is a function of incident angle (θ ), F hkl is the structure factor for a specific crystal
plane, v is the unit cell volume of the crystal and the temperature factor is e − 2M ,
and p is the multiplicity factor of a crystal, which is the number of crystal planes
that have the same plane spacing. For a cubic crystal, the p value of {001} is six and
the p value of {111} is eight, because there are six and eight planes in the plane
family, respectively. The temperature factor can be extracted from Figure 2.27.
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74
1.0
e−2M
0.9
0.8
0.7
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
sin θ (Å−1)
λ
Figure 2.27 Temperature factor (e − 2M ) is a function of diffraction angle and wavelength.
(Reproduced with permission from Ref. [1].)
Similarly, we have a peak intensity of β phase in the mixture.
Iβ =
K 2 R β Cβ
μm
(2.15)
Under identical conditions of X-ray source and incident intensity, the constant K 2
should be the same. Thus, the following relationship holds.
R C
Iα
= α α
Iβ
R β Cβ
(2.16)
Equation (2.16) simply tells us how to obtain the ratio of weight fractions of α and
β phases from their ratio of peak intensity, as long as the R values of individual
peaks in the mixture are calculated. We can also apply this method to a mixture
containing more than two phases, because the following condition always holds.
Ci = 1
i
This method does not require powder samples. Thus, it is convenient for estimating
phase contents in polycrystalline solids.
2.4
Wide-Angle X-Ray Diffraction and Scattering
Wide-angle X-ray diffraction (WAXD) or wide-angle X-ray scattering (WAXS) is the
technique that is commonly used to characterize crystalline structures of polymers
and fibers. The technique uses monochromatic X-ray radiation to generate a
transmission diffraction pattern of a specimen that does strongly absorb X-rays,
such as an organic or inorganic specimen containing light elements. WAXD or
scattering refers to X-ray diffraction with a diffraction angle 2θ > 5◦ , distinguishing
it from the technique of small-angle X-ray scattering (SAXS) with 2θ < 5◦ . SAXS
75
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2.4 Wide-Angle X-Ray Diffraction and Scattering
2 X-Ray Diffraction Methods
will not be discussed in this chapter because its complexity in theoretical treatment
is beyond the scope of this book.
2.4.1
Wide-Angle Diffraction
Figure 2.28 illustrates the optical arrangement of WAXD. The incident X-ray beam
is formed after X-rays pass through a monochromator and a collimator (not shown
in Figure 2.28). The highly monochromatic and parallel X-ray beam strikes a
sample and generates a diffracted beam at angle 2θ i with respect to the transmitted
beam. The diffracted beams are recorded as an image on a film or by an area
detector that is placed at distance D from the specimen and perpendicular to the
incident beam direction. Usually, there is a beam-stop (made from lead) placed in
front of the film or detector center to prevent the transmitted beam from striking
the film or area detector directly. Thus, WAXD is a photographic method, differing
from the spectroscopic methods of diffractometry. Small-angle scattering uses the
same optical arrangement as WAXD, except that D is longer in order to record
scattering from small 2θ angles.
The Bragg angle θ i is determined by a simple geometric relationship
1 1
tan (Ri /D)
(2.17)
2
where Ri is the distance between the transmitted beam and the diffracted beam
on the recording film plane as shown in Figure 2.28. The d-spacing of the
crystallographic plane generating diffraction is calculated according to Bragg’s
Law.
λ
(2.18)
d=
2 sin[{tan−1 (Ri /D)}/2]
θi =
Film
or d
ete
ctor
plan
e
Transmitted beam
na
io
id
er
Sample
Ri
ne
la
lp D
M
torial
Equa
plane
Diffracfted beam
nt
ide
m
ea
b
Inc
Figure 2.28
Diffraction geometry of wide-angle X-ray diffraction (WAXD).
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76
The accuracy of d-spacing measurement relies on the measurement of R and D. A
reliable method for determining D is to calculate it from Eq. (2.18) with a known
d-spacing of crystal, not from a direct measurement. Ri is commonly obtained by
measuring 2Ri on a film in order to avoid the problem of determining the center
of the transmitted beam on the film.
One of the main reasons for using WAXD for polymer analysis is that crystalline
polymers are frequently presented in the form of fibers with preferential crystal
orientation with respect to the fiber axis; for example, the a–b crystallographic plane
is perpendicular to the fiber axis that is along a vertical direction in Figure 2.28.
WAXD analysis can readily reveal the preferential orientation of polymer crystals
for a diffraction pattern recorded on the film. Figure 2.29 illustrates the generation
of such a diffraction pattern of highly oriented polymer crystals using the Ewald
sphere. The orientation of crystals with a–b planes perpendicular to a fiber axis can
be represented by the reciprocal lattice of the crystals with c* perpendicular to the
incident beam. The a–c or b–c planes of crystals can be randomly oriented in the
fiber. Collective reciprocal lattices of the crystals with alignment of the a–b plane
normal along the fiber axis but with random orientation of a–c and b–c planes
are equivalent to rotating the reciprocal lattices around the c* -axis. These collective
reciprocal lattices form a series of cocentered rings, as shown in Figure 2.29.
As illustrated in Figure 2.10, the intersections between the rings of reciprocal
lattices and the surface of the Ewald sphere generate diffraction. Consequently,
the oriented crystals in a fiber generate a diffraction pattern, as shown in the film
plane of Figure 2.29. The diffraction spots on the equatorial plane represent the
diffraction of [hk0] planes. A line of diffraction spots above or below the equatorial
plane should represent the diffraction of (hk1) planes or (hk1) planes, respectively.
Fil
m
or
de
tec
tor
Ewald sphere
c∗
M
pla
ne
I
Incident
X-ray beam
O
E
Reciprocal lattice rotating
along c ∗ axis
Figure 2.29 A WAXD pattern of highly oriented polymer crystals with their reciprocal
lattices and the Ewald sphere.
77
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2.4 Wide-Angle X-Ray Diffraction and Scattering
2 X-Ray Diffraction Methods
Figure 2.30 A WAXD pattern of Kevlar, poly-(p-phenylene terephthalamide), fibers. (Reproduced with permission from Ref. [1].)
The diffraction principles of oriented crystals discussed here apply to all types
of samples through which X-rays can be transmitted, even though the main
applications of WAXD are for crystalline polymers and proteins (special types of
polymers). The most famous application to proteins is probably the determination
of the DNA double helix structure.
Figure 2.30 shows an example of a WAXD pattern of Kevlar fibers. The fiber axis
is perpendicular to the incident X-ray beam and aligned in the meridianal plane.
The [hkl] diffraction spots are mainly located on the meridianal plane with high
symmetry with respect to the equatorial plane. Figure 2.31 shows another example
HA
(211, 112, 300)
PE
(110)
HA
(002)
PE
(200)
Figure 2.31 A WAXD pattern of a composite sample containing ultrahigh molecular weight
polyethylene (PE) fibrils and nanoparticles of hydroxyapatite (HA). The arrow indicates the
drawing direction in the composite sample.
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78
of a WAXD pattern of a composite with ultrahigh molecular weight polyethylene
(UHMWPE) fibrils and nanosized ceramic particulates. The composite sample has
been mechanically drawn in order to increase alignment of UHMWPE fibrils. The
composite sample is perpendicular to the incident beam but the fibrils are aligned
with a drawing direction marked on the pattern. The WAXD pattern revealed the
preferential orientation of UHMWPE crystals and the perfectly random orientation
of ceramic particles. A digital area detector provides a high-contrast WAXD pattern
as shown in Figure 2.31.
2.4.2
Wide-Angle Scattering
Intensity
The terms ‘‘wide-angle X-ray scattering’’ and ‘‘wide-angle X-ray diffraction’’ are often
used without clear distinction because there is little difference in their instrumentation. However, ‘‘scattering’’ is a more general term than ‘‘diffraction’’ that
refers to constructive interference of scattered rays from crystallographic planes.
WAXS is considered to be an appropriate technique for examining both crystalline
and noncrystalline materials. WAXS is particularly useful for polymers because a
noncrystalline (amorphous) structure is the common characteristic of polymers,
even for crystalline polymers because they are not totally crystalline.
An amorphous material can generate a diffraction spectrum in a 2θ range, as
shown schematically in Figure 2.32. For an amorphous polymer, sharp diffraction
peaks are absent from its diffraction spectrum, only showing a wide halo peak.
Although there is a lack of diffraction peaks from crystallographic planes, an amorphous polymer may exhibit scattering-intensity variations because of fluctuations
in electron density over a certain length scale. The fluctuations in electron density
of polymers result from heterogeneity of their mass and chemical distributions at
the microscopic level. WAXS is used to detect microscopic features less than about
10 nm in length, compared with SAXS that is often used to examine microscopic
features greater than about 50 nm.
WAXS is commonly presented with scattering-intensity curves over a range
of scattering vector magnitude as shown in Figure 2.33, or two-dimensional (2D)
Waxs
Saxs
Amorphous
halo
2θ (degree)
Figure 2.32 X-ray scattering by amorphous materials showing the difference in range of
small-angle and wide-angle scattering.
79
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2.4 Wide-Angle X-Ray Diffraction and Scattering
Intensity
2 X-Ray Diffraction Methods
1
2
3
Scattering vector magnitude (Å−1)
6
Equatorial
meridin
Scattering vector magnitude (Å−1)
Figure 2.33 WAXS curves for poly(tetrafluoroethylene) in crystalline phase (dashed line)
and in the amorphous phase (solid line). (Reproduced with permission from Ref. [1].)
5
4
Meridional
equator
3
2
1
1
2
3
4
5
6
Scattering vector magnitude (Å−1)
1
2
3
4
5
6
Scattering vector magnitude (Å−1)
Figure 2.34 (a) WAXS map and (b) curve for partially aligned noncrystalline polyetheretherketone (PEEK) prepared by extrusion. (Reproduced with permission from Ref. [1].)
scattering intensity maps as shown in Figure 2.34. The scattering vector magnitude
is equal to 4π(sin θ )λ− 1 . The scattering vector magnitude is approximately proportional to the length of Ri in Figure 2.28; however, it is independent of the distance
between the sample and detector plane. We may interpret a WAXS curve or map
as the scattering-intensity variation along the radial direction in the detector plane
(Figure 2.28).
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80
Figure 2.33 shows an example of WAXS curves for a polymer (polytetrafluoroethylene). It is a crystalline polymer at room temperature and its crystalline
structure is revealed by the sharp peaks, as shown by the dashed line in Figure
2.33. The polymer becomes an amorphous molten phase at elevated temperature;
consequently, the peaks disappear and become a broad ‘‘hilly’’ curve as shown
by the solid line. Figure 2.34 shows an example of WAXS presentation with a
2D map (Figure 2.34a) and also scattering intensity curves along two perpendicular directions (Figure 2.34b). The WAXS intensities of extruded noncrystalline
polyetheretherketone (PEEK) indicate a certain degree of microstructural alignment along the extrusion direction. The alignment is revealed by the difference in
the scattering intensity at about 1.3 Å−1 in the equatorial and meridianal directions.
The difference is shown in both the intensity contours in the 2D map and the
intensity curves along the equatorial and meridianal directions.
Questions
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
Calculate the 2θ values in the X-ray diffraction spectrum for aluminum
(FCC). Assume the X-ray radiation is CuKα 1 .
Calculate the 2θ values in the X-ray diffraction spectrum for iron (BCC).
Assume the X-ray radiation is CuKα 1 .
Calculate the shifts in 2θ values in the diffraction spectrum in Question 2.1
by CuKα 2 radiation.
Show that a relationship between real and reciprocal lattice is:
r • d* = uh + vk + wl = m (m is an integer).
Sketch a two-dimensional plane of the reciprocal lattice for an orthorhombic
crystal (in which a > b) with a plane normal to the [001].
Sketch a two-dimensional plane of the reciprocal lattice for a hexagonal
crystal with a plane normal as [001].
Calculate the structure factor of extinction for a hexagonal close-packed
(HCP) structure. There are two atoms per unit cell at (000) and at 13 , 23 , 12
respectively.
Why does the background intensity of an X-ray spectrum decrease with 2θ ?
Is the peak density (number of peaks per 2θ angle) higher at low 2θ or at
high 2θ in X-ray diffraction spectra? Why? Use a cubic crystal as an example
to interpret this phenomenon.
Explain possible reasons to cause discrepancies between the peak positions
of an X-ray spectrum and its standard data.
If diffraction peaks of a crystalline solid shift to the high 2θ direction by
internal stress, is this tensile or compressive stress?
Explain possible reasons to cause discrepancies between the peak intensities
of an X-ray spectrum and its standard data.
A thin-film polycrystalline solid has a preferential orientation with [001]
perpendicular to its specimen surface. Which kind of [hkl] will exhibit the
81
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2.4 Wide-Angle X-Ray Diffraction and Scattering
2 X-Ray Diffraction Methods
higher peak intensity and which kind of [hkl] will exhibit lower peak intensity
than a standard spectrum of the same solid?
References
von Heimandahl, M. (1980) Electron Microscopy of Materials, Academic Press, New
York.
Lifshin, E. (1999) X-Ray Characterization
of Materials, Wiley-VCH Verlag GmbH,
Weinheim.
Eberhart, J.P. (1991) Structural and Chemical
Analysis of Materials, John Wiley & Sons,
Ltd, Chichester.
Als-Nielsen, J. and McMorrow, D. (2001) Elements of Modern X-Ray Physics, John Wiley
Further Reading
& Sons, Inc., New York.
Baltá-Calleja, F.J. and Vonk, C.G. (1989)
Callister, W.D. (2000) Materials Science and
X-Ray Scattering of Synthetic Polymers,
Engineering: An Introduction, 7th edn, John
Elsevier, Amsterdam.
Wiley & Sons, Inc., New York.
1. Cullity, B.D. and Stock, S.R. (2001) El-
ements of X-Ray Diffraction, 3rd edn,
Prentice Hall, Upper Saddle River,
NJ.
2. Jenkins, R. and Snyder, R.L. (1996)
Introduction to X-Ray Powder Diffractometry, John Wiley & Sons, Inc.,
New York.
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82
3
Transmission Electron Microscopy
Electron microscopes generate images of material microstructures with much
higher magnification and resolution than light microscopes. The high resolution
of electron microscopes results from the short wavelengths of the electrons used
for microscope illumination. The wavelength of electrons in electron microscopes
is about 10,000 times shorter than that of visible light. The resolution of electron
microscopes reaches the order of 0.1 nm if lens aberrations can be minimized.
Such high resolution makes electron microscopes extremely useful for revealing
ultrafine details of material microstructure. There are two main types of electron
microscopes: transmission electron microscopes (TEMs) and scanning electron
microscopes (SEMs). The optics of the TEM is similar to the conventional transmission light microscope, while that of a SEM is more like that of scanning
confocal laser microscopes. This chapter introduces the basic working principles
and features of TEMs.
3.1
Instrumentation
A TEM, similar to a transmission light microscope, has the following components
along its optical path: light source, condenser lens, specimen stage, objective lens,
and projector lens, as shown in Figure 3.1. The main differences are that, in a
TEM, the visible light ray is replaced by an electron ray and glass lenses for visible
light are replaced by electromagnetic lens for the electron beam. The TEM has
more lenses (the intermediate lens) and more apertures (including the selectedarea aperture). The TEM contains further features arising from using electrons as
illumination. For example, a vacuum environment is required in a TEM because
collisions between high-energy electrons and air molecules significantly absorb
electron energy. Table 3.1 provides a comparison of a TEM with a light microscope.
The structural features of the TEM are introduced in detail in the following
sections.
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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83
3 Transmission Electron Microscopy
High vacuum
Electron gun
Accelerator
Illumination
1st condenser lens
2nd condenser lens
Specimen stage
Imaging
Specimen
Objective lens
Intermediate lens
Magnification
Projector lens
Data recording
Figure 3.1
Fluorescent screen
Photographic film
CCD camera
Structure of a transmission electron microscope and the optical path.
3.1.1
Electron Sources
In a TEM system, an electron gun generates a high-energy electron beam for
illumination. In the electron gun, the electrons emitted from a cathode, a solid
surface, are accelerated by high voltage (V o ) to form a high-energy electron beam
with energy E = eV o . Because electron energy determines the wavelength of the
electrons and wavelength largely determines the resolution of the microscope
(Eq. (1.3)), the acceleration voltage determines the resolution to a large extent.
Table 3.2 gives the relationship between the acceleration voltage and wavelength. It
also provides the correlation between acceleration voltage and the TEM resolution,
which is calculated with a realistic α angle of about 6.5 × 10−3 rad. To achieve a high
resolution, the TEM is usually operated under an acceleration voltage of greater
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84
Table 3.1
Comparison between light and transmission electron microscopes.
Specimen requirements
Best resolution
Magnification range
Source of illumination
Lens
Operation environment
Image formation for viewing
Table 3.2
Transmission electron
microscope
Polished surface and
thin section (<100 μm)
∼200 nm
2–2 000×
Visible light
Glass
Air or liquid
By eye
Thin section (<200 nm)
∼0.2 nm
500–1 000 000×
High-speed electrons
Electromagnetic
High vacuum
On phosphorescent plate
Correlation between acceleration voltage and resolution.
Acceleration voltage (kV)
40
60
80
100
200
500
Transmission light
microscope
Electron wavelength (nm)
TEM resolution (nm)
0.00601
0.00487
0.00418
0.00370
0.00251
0.00142
0.56
0.46
0.39
0.35
0.24
0.13
than 100 kV. In practice, 200 kV is commonly used and meets most resolution
requirements. High-voltage electron microscopy (∼1000 kV) requires extremely
expensive instrumentation, and also it may damage a specimen by generating
microstructural defects in it during observation because of its high electron
energy.
The general structure of an electron gun is composed of three main parts: a
cathode or electron source, a Wehnelt electrode, and an anode, as illustrated in
Figure 3.2. Electrons are emitted from the surface of the cathode and accelerated
by an electric field toward the anode. The Wehnelt electrode is placed between the
cathode and the anode. It is biased a few hundred volts negative with respect to
the cathode in order to stabilize the electron beam against voltage fluctuation by
reducing the electron beam current whenever necessary. There are two basic types
of electron guns: thermionic emission and field emission.
3.1.1.1 Thermionic Emission Gun
This is the most common type of electron gun and includes the tungsten filament
gun and the lanthanum hexaboride gun. The tungsten gun uses a tungsten filament
as the cathode. During operation, the filament is heated by an electrical current
85
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3.1 Instrumentation
3 Transmission Electron Microscopy
Cathode
Wehnelt
electrode
Anode
Figure 3.2
General structure of an electron gun.
(filament current) to high temperature (∼2800 K). The high temperature provides
kinetic energy for electrons to overcome the surface energy barrier, enabling the
conduction electrons in the filament to leave the surface. The electrons leaving the
surface are accelerated by a high electrical voltage between the filament and anode
to a high energy level. The intensity of the electron beam is determined by the
filament temperature and acceleration voltage.
Lanthanum hexaboride (LaB6 ) is a better cathode than tungsten and it is more
widely used in modern electron microscopes. Electrons require less kinetic energy
to escape from the LaB6 surface because its surface work function is about 2 eV,
smaller than the 4.5 eV of tungsten. Thus, a lower cathode temperature is required.
A LaB6 cathode can generate a higher intensity electron beam and has a longer
life than a tungsten filament. One disadvantage is that a higher level of vacuum is
required for a LaB6 gun than for a tungsten filament gun.
3.1.1.2 Field Emission Gun
This type of electron gun does not need to provide thermal energy for electrons
to overcome the surface potential barrier of electrons. Electrons are pulled out by
applying a very high electric field to a metal surface. A tunneling effect, instead of a
thermionic effect, makes metal electrons in the conducting band cross the surface
barrier. During operation, electrons are physically drawn off from a very sharp tip
of a tungsten crystal (∼100 nm tip radius) by an applied voltage field. The field
emission gun generates the highest intensity electron beam, 104 times greater than
that of the tungsten filament gun and 102 times greater than that of the LaB6 gun.
There are two kinds of field emission guns: thermal and cold guns. The thermal
field emission gun works at an elevated temperature of about 1600–1800 K, lower
than that of thermionic emission. It provides a stable emission current with less
emission noise. The cold field emission gun works at room temperature. It provides
a very narrow energy spread (about 0.3–0.5 eV), but it is very sensitive to ions in air.
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86
Table 3.3
Comparison of electron guns.
Tungsten filament
Field emission
LaB6
Operation temperature (K)
Brightnessa at 200 kV (A cm−2 sr)
Requirement for vacuum (torrb)
a
b
∼2800
∼5 × 105
10−4
Thermal
Cold
∼1800
1600–1800
∼300
∼5 × 106
∼5 × 108
∼5 × 108
10−6 −10−7
10−9
10−9 −10−10
Intensity emitted per unit cathode surface in unit solid angle.
1 torr = 133 Pa.
The bombardment of the tungsten tip by residual gaseous ions causes instability
of the emission. Thus, regular maintenance (called flashing) of the tip is necessary.
Generally, a vacuum of 10−10 torr is required to operate the cold field emission
gun. Table 3.3 shows a comparison of various kinds of electron guns.
3.1.2
Electromagnetic Lenses
Lenses in light microscopes are made of glass; however, glass lenses cannot be used
in electron microscopes because glass does not deflect or focus an electron beam.
Noting that electrons have electric charges and that electric charges interact with
magnetic fields, we can use a magnetic force to deflect or focus an electron beam.
All lenses in an electron microscope are electromagnetic. Figure 3.3 illustrates the
basic structure of an electromagnetic lens. The lens consists of a case and two
poles. The case is made of soft-magnetic material, and encloses a solenoid. The
Coil
N
N
S
S
Coil
Electron
lens
f
Figure 3.3 Structure of an electromagnetic lens. The magnetic field concentrated between
the N and S poles deflects the electron beam.
87
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3.1 Instrumentation
3 Transmission Electron Microscopy
poles are two pieces located at the narrow annular opening of the case; they are
machined to very precise tolerances.
Such an arrangement creates a powerful magnetic field concentrated in the
gap between the two pole pieces (N and S). Thus, when an electron beam passes
through the lens, it is focused and deflected by the field’s magnetic lines of force.
Since the strength of a magnetic field can be easily manipulated by altering the
electric current that generates the magnetic field, an electromagnetic lens has a
special advantage over a glass lens: the magnification power of an electromagnetic
lens can be altered by simply changing the current passing through the solenoid of
the lens.
The lens system of a TEM is more complicated than a light microscope, besides
the electromagnetic lenses. There are two or more condenser lenses to demagnify
the electron beam emitted from the electron gun. The condenser lens system
controls the beam diameter and convergence angles of the beam incident on a
specimen. During operation, the illumination area of specimen and illumination
intensity can be adjusted by controlling the current in the electromagnetic lenses of
condensers. The TEM has three lenses to ensure a magnification capability of about
105 –106 times: objective, intermediate, and projector lenses. The intermediate lens
is used to switch the TEM between an image mode and a diffraction mode that will
be discussed in Section 3.4 For the image mode, the intermediate lens is focused
on the image plane of the objective lens, and for the diffraction mode it is focused
on the back-focal plane of the objective lens where the diffraction pattern forms.
Specimen
Objective lens
Reciprocal space
SAD
Objective
aperture
Real space
Intermediate lens
Second
intermediate
image
(a)
(b)
Figure 3.4 Optical paths of: (a) diffraction mode and (b) image mode. SAD, selected-area
diffraction aperture.
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88
Figure 3.4 schematically illustrates the switch between optical paths for image
and diffraction modes by using the intermediate lens. The projector lens further
magnifies the image or diffraction pattern and projects it onto the fluorescent
screen for observation or the photographic plane.
The aperture of an electron microscope is a piece of metal with a small hole
in the center, similar to that in a light microscope. The primary functions of the
aperture are to limit light scattering and/or to select the nondiffracted or diffracted
beams. The objective aperture in a TEM is located in the gap between the pole
pieces of the electromagnetic lens, as illustrated in Figure 3.5. The hole diameter
of the objective aperture in the TEM is only of the order of tens of micrometers.
3.1.3
Specimen Stage
The TEM has special requirements for specimens to be examined; it does not
have the same flexibility in this regard as light microscopy. TEM specimens must
be a thin foil because they should be able to transmit electrons; that is, they are
electronically transparent. A thin specimen is mounted in a specimen holder, as
shown in Figure 3.6, in order to be inserted into the TEM column for observation.
The holder requires that a specimen is a 3-mm disc. Smaller specimens can be
mounted on a 3-mm mesh disc, as illustrated in Figure 3.7. The meshes, usually
made from copper, prevent the specimens from falling into the TEM vacuum
column. Also, a copper mesh can be coated with a thin film of amorphous carbon
in order to hold specimen pieces even smaller than the mesh size.
The specimen holder is a sophisticated, rod-like device that not only holds the
specimen but also is able to tilt it for better viewing inside the TEM column. Types
of specimen holders used include single-tilt and double-tilt. The single-tilt holder
allows a specimen to be titled along one axis in the disc plane. The double-tilt holder
Stray
electrons
Coil
Upper
pole piece
Lower
pole piece
Aperture
Lens
axis
Figure 3.5 The objective aperture located in the electromagnetic lens.
89
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3.1 Instrumentation
3 Transmission Electron Microscopy
Figure 3.6 A specimen holder for a TEM (JEM-2010F) with a double-tilting function. The
insert shows the enlarged part of the holder end where the 3-mm disc of the specimen is
installed.
Figure 3.7
A metal mesh disc supporting small foil pieces of a specimen.
allows the specimen be tilted independently along two axes in the disc plane. The
double-tilt holder is necessary for analytical studies of crystalline structures.
3.2
Specimen Preparation
Preparation of specimens often is the most tedious step in TEM examination. To
be electronically transparent, the material thickness is limited. We have to prepare
a specimen with at least part of its thickness at about 100 nm, depending on the
atomic weight of the specimen materials. For higher atomic weight material, the
specimen should be thinner. A common procedure for TEM specimen preparation
is described as follows.
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90
3.2.1
Prethinning
Prethinning is the process of reducing the specimen thickness to about 0.1 mm
before final thinning to 100 nm thickness. First, a specimen less than 1 mm thick
is prepared. This is usually done by mechanical means, such as cutting with
a diamond saw. Then, a 3-mm diameter disc is cut with a specially designed
punch before further reduction of thickness. Grinding is the most commonly
used technique to reduce the thickness of metal and ceramic specimens. During
grinding, we should reduce the thickness by grinding both sides of a disc, ensuring
the planes are parallel. This task would be difficult without special tools. Figure 3.8
shows a hand-grinding jig for prethinning. The disc (S) is glued to the central post
and a guard ring (G) guides the grinding thickness. A dimple grinder is also used
for prethinning, particularly for specimens that are finally thinned by ion milling,
which is introduced in Section 3.2.2.2.
3.2.2
Final Thinning
Three methods of final thinning are described here: electrolytic thinning for metal
specimens that are good electric conductors, ion milling for metal and ceramic
specimens, and ultramicrotome cutting for polymeric and biological specimens.
3.2.2.1 Electrolytic Thinning
Electrolytic thinning and ion milling are methods for reducing specimen thickness
to the scale of 100 nm. These methods create a dimpled area on prethinned
specimens because it is almost impossible to reduce the thickness of specimens
uniformly to the level of electron transparency. The dimpled area is likely to have
G
S
Figure 3.8 Hand-grinding jig for TEM specimen preparation. A disc (S) is glued to the
center of the jig and the guide ring (G) controls the amount of grinding.
91
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3.2 Specimen Preparation
3 Transmission Electron Microscopy
regions of electron transparency, as schematically shown in Figure 3.9. Electrolytic
thinning is widely used for preparing specimens of conducting materials. A
specimen is placed in an electrochemical cell with the specimen as the anode.
A suitable electrolyte (usually an acidic solution) is used to electrochemically
reduce the specimen thickness. A common technique is jet polishing, illustrated
schematically in Figure 3.10. A specimen is placed in a holder with two sides facing
guides of electrolyte jet streams, which serve as the cathode. The electrolyte jet
polishes both sides of the specimen until light transparency is detected by a light
detector. Catching the precise moment that tiny holes appear is crucial, because
only the edge of a tiny hole contains thin areas that are electron transparent.
Electrolytic thinning is very efficient and is completed in only 3–15 min.
3.2.2.2 Ion Milling
Ion milling uses a beam of energetic ions to bombard specimen surfaces in order to
reduce the thickness by knocking atoms out of a specimen. The specimen does not
need to be electrically conductive for ion milling. Thus, the technique is suitable
for metal, ceramics, and other materials, as long as they are thermally stable.
Figure 3.11 illustrates the general procedure of ion milling. Before ion milling, the
specimen is often ground with a dimple grinding device in order to reduce the
thickness in the central are of specimen (Figure 3.11a). Then, the ground specimen
is cut as a 3-mm disc and placed in the ion-milling chamber with a geometric
arrangement, as shown in Figure 3.11b. The edge of the specimen disc may need to
3 mm
∼0.15 mm
Electron-Transparent Zone
Figure 3.9
A dimple in the center of a specimen disc.
Anode
Sample holder for disk
specimen (2.3 or 3.0 mm diameter)
Jet (cathode) stream
(1-1.5 mm diameter)
Light guide
(3 mm diameter)
Figure 3.10 Electrochemical jet-polishing schematic diagram. (Reproduced with permission
from Ref. [1]. © 1980 Elsevier B. V.)
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92
Grinder
Diamond paste
Specimen
(a)
Glass
Laser
autoterminator
Specimen
Ar ion
Mo mesh
(b)
Laser light
Figure 3.11 Ion thinning process: (a) dimple grinding and (b) ion milling. (Reproduced
with kind permission of Springer Science and Business Media from Ref. [2]. © 2002
Springer-Verlag GmbH.)
be covered by a molybdenum ring in order to strengthen it during ion milling. An
ion beam with energy of 1–10 keV bombards the specimen. The specimen is placed
in the center at an angle of about 5–30◦ to the ion beam in order have a high yield
of sputtering. Light transparency is detected by a light detector aligned along the
vertical direction. The ion beam can raise the temperature of the specimen rapidly
and dramatically. Thus, cooling the chamber with liquid nitrogen is necessary in
order to prevent specimen heating by the ion beam. Even with cooling, organic
materials are not suitable for ion milling because the ion beam can cause severe
damage to the microstructure of organic specimens such as polymers.
3.2.2.3 Ultramicrotomy
Ultramicrotomy is basically the same type of method as microtomy for preparing
soft specimens for light microscopy. However, ultramicrotomy can be used to
section a specimen to the 100 nm scale. It is commonly used to prepare polymeric
or biological TEM specimens. Figure 3.12 illustrates the working principles of the
instrument. A specimen is mounted in a holder against the cutting tool (glass
93
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3.2 Specimen Preparation
3 Transmission Electron Microscopy
Specimen block trimmed
Diamond knife
Arm
Back-and-forth motion
Sections
Water
Up-and-down
motion
Boat
Figure 3.12 Schematic of ultramicrotomy. (Reproduced with kind permission of Springer
Science and Business Media from Ref. [2]. © 2002 Springer-Verlag GmbH.)
knife or diamond knife). The specimen should be trimmed to have a tip held
against the knife. The cross section of the trimmed tip usually is only about 1 mm2
for diamond knife cutting. The holder gradually moves toward the knife while
it repeatedly moves up and down. The firmly mounted specimen is sectioned
as it passes the edge of the knife blade. To be sectioned by an ultramicrotome,
materials must be softer than the knife. Even though diamond is the hardest
material available, a specimen can still damage the tip of a diamond knife because
the extremely sharp tip of a diamond knife makes it very fragile.
The aforementioned TEM specimen preparation techniques do not include all
those that have been used. Various unique methods have been created for specific
types of materials. For example, hammering has been used for very ductile metal
such as gold, cleaving for materials such as mica and graphite flakes, and chemical
thinning with suitable acids for nonmetallic materials. A ceramic specimen can
be prepared by extracting its precipitates and separating them from a substrate
with ultrasonic force in a liquid environment. This preparation technique avoids
difficulties in thinning ceramic bulk materials. Success in TEM examination heavily
relies on the quality of specimen preparation; thus, successful innovation in TEM
specimen preparation can bring huge rewards.
3.3
Image Modes
As mentioned in Chapter 1, an observable image must display sufficient contrast (a brightness difference between two adjacent image points). Contrast in
transmission-light microscopy is generated by differences in light absorption in
different regions of the specimen. In TEM, however, absorption of electrons plays
a very minor role in image formation. TEM contrast relies instead on deflection
of electrons from their primary transmission direction when they pass through
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94
the specimen. The contrast is generated when there is a difference in the number of electrons being scattered away from the transmitted beam. There are two
mechanisms by which electron scattering creates images: mass–density contrast and
diffraction contrast.
3.3.1
Mass–Density Contrast
The deflection of electrons can result from interaction between electrons and
an atomic nucleus. Deflection of an electron by an atomic nucleus, which has
much more mass than an electron, is like a collision between a particle and a
wall. The particle (electron) changes its path after collision. The amount of electron
scattering at any specific point in a specimen depends on the mass–density (product
of density and thickness) at that point. Thus, differences in thickness and density
in a specimen will generate variations in electron intensity received by an image
screen in the TEM, if we only allow the transmitted beam to pass the objective
aperture as shown in Figure 3.13. The deflected electrons with scattering angle
larger than the α angle (of the order of 0.01 rad) controlled by the objective aperture
will be blocked by the aperture ring. Thus, the aperture reduces the intensity of
the transmission beam as the beam passes through it. The brightness of the image
is determined by the intensity of the electron beam leaving the lower surface of
the specimen and passing through the objective aperture. The intensity of the
transmitted beam (It ) is the intensity of primary beam (Io ) less the intensity of
Primary beam
Sample
Scattered
Id
beams
Objective lens
Objective aperture
It
Additional magnifying
lenses
A
Intensity profile
on the screen
B
Fluorescent screen
Bright
Dark
Figure 3.13 Optical arrangement of mass–density contrast in the TEM. (Reproduced with
permission from Ref. [1]. © 1980 Elsevier B. V.)
95
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3.3 Image Modes
3 Transmission Electron Microscopy
beam deflected by object (Id ) in a specimen.
It = Io − Id
(3.1)
The contrast (C) in a TEM is defined by Eq. (3.2).
C = (Io − It )/Io
(3.2)
This type of mass–density contrast exists in all types of materials. It is the main
mechanism for image formation for noncrystalline materials such as amorphous
polymers and biological specimens. The mass–density contrast is also described
as ‘‘absorption contrast,’’ which is rather misleading because there is little electron
absorption by the specimen.
In order to increase contrast, polymeric and biological specimens often are stained
by solutions containing high-density substances such as heavy-metal oxides. The
ions of metal oxides in solution selectively penetrate certain constituents of the
microstructure, and thus increase its mass–density. Figure 3.14 is an example
of a TEM image showing mass–density contrast in a specimen of polymer blend
containing polycarbonate (PC) and polybutylene terephthalate (PBT). The PC phase
appears darker because it is rich in staining substance, RuO4 . Besides staining,
common effective techniques to increase contrast include using a smaller objective
aperture and using a lower acceleration voltage. The negative side of using such
techniques is reduction of total brightness.
3.3.2
Diffraction Contrast
We can also generate contrast in the TEM by a diffraction method. Diffraction contrast is the primary mechanism of TEM image formation in crystalline specimens.
Diffraction can be regarded as collective deflection of electrons. Electrons can be
scattered collaboratively by parallel crystal planes similar to X-rays. Bragg’s Law (Eq.
(2.1)), which applies to X-ray diffraction (XRD), also applies to electron diffraction.
When the Bragg conditions are satisfied at certain angles between electron beams
and crystal orientation, constructive diffraction occurs and strong electron deflection in a specimen results, as schematically illustrated in Figure 3.15. Thus, the
intensity of the transmitted beam is reduced when the objective aperture blocks
the diffraction beams, similar to the situation of mass–density contrast. Note that
the main difference between the two contrasts is that the diffraction contrast is very
sensitive to specimen tilting in the specimen holder but mass–density contrast is
only sensitive to total mass in thickness per surface area.
The diffraction angle (2θ ) in a TEM is very small (≤1◦ ) and the diffracted
beam from a crystallographic plane (hkl) can be focused as a single spot on the
back-focal plane of the objective lens. The Ewald sphere is particularly useful for
interpreting electron diffraction in the TEM. When the transmitted beam is parallel
to a crystallographic axis, all the diffraction points from the same crystal zone will
form a diffraction pattern (a reciprocal lattice) on the back-focal plane as shown in
Figures 2.9 and 2.11.
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96
PC
PBT
Crack
Crack Tip
1 μm
PBT
PC
Craze
1 μm
Figure 3.14 TEM image of PC–PBT polymer blends with mass–density contrast. The specimen is stained with RuO4 . (Reproduced with permission of Jingshen Wu.)
The diffraction contrast can generate bright-field and dark-field TEM images.
In order to understand the formation of bright-field and dark-field images, the
diffraction mode in a TEM must be mentioned. A TEM can be operated in two
modes: the image mode and the diffraction mode. We can switch between the
modes by changing the optical path in the TEM, as illustrated in Figure 3.4. In the
image mode, the image of the specimen is focused and projected onto a fluorescent
screen. In the diffraction mode, the diffraction pattern formed on the back-focal
plane is projected onto a fluorescent screen as shown in Figure 3.16. The TEM
97
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3.3 Image Modes
3 Transmission Electron Microscopy
Primary beam I0
I0
Sample
2θ
Ir
f
Objective lens
Back focal plane
Ir
Objective aperture
α
Plane of diffraction pattern
Ir = Diffracted beam
Transmitted beam Id
Image plane (single-stage
magnified image)
(a)
I0
Crystalline object,
containing inclusion
Bragg
diffraction
(b)
Diffraction
from inclusion
Figure 3.15 Electron deflection by Bragg diffraction of a crystalline specimen: (a) image
formation in crystalline samples and (b) diffraction at crystal lattice planes and at the contours of inclusions. (Reproduced with permission from Ref. [1]. © 1980 Elsevier B. V.)
diffraction pattern shown in Figure 3.16 exhibits a plane of the reciprocal lattice of
crystal (Section 2.1.1). Such a pattern is obtained by diffraction from a selected area
in the specimen that contains a single crystal. The diffraction mode is designed for
selected-area diffraction (SAD), which is discussed further in Section 3.4.
A bright-field image is obtained by allowing only the transmitted beam to pass
the objective aperture, exactly the same as in mass–density contrast. A dark-field
image, however, is obtained by allowing one diffraction beam to pass the objective
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98
Figure 3.16 Photograph of a typical electron diffraction pattern of single crystal. The transmitted spot at the center is much brighter than the diffraction spots.
aperture. Figure 3.17 illustrates the optical arrangement of bright- and dark-field
contrast. To switch between bright- and dark-field modes, we need to operate in the
diffraction mode first in order to select one diffraction spot in the diffraction pattern
by moving the aperture to the center of that spot (Figure 3.18). However, what really
happens in the TEM is that the direction of the incident beam is moved, rather than
the aperture, to shift the selected diffraction spot to the central axis (Figure 3.17c).
Io
Io
Io
2θ
2θ
2θ
It
Id
(a)
It
(b)
Id
It
(c)
Id
Figure 3.17 Arrangement for: (a) bright-field image and (b,c) dark-field image.
Transmitted
Diffracted
(a)
Objective aperture
(b)
Figure 3.18 Selection of a diffraction spot with an objective aperture for dark-field imaging.
99
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3.3 Image Modes
3 Transmission Electron Microscopy
V
3
3
2
2
4
4
I
(a)
1
(b)
Figure 3.19 Bright-field images of aluminum alloy. The contrast difference between (a)
and (b) is generated by tilting the specimen. Individual grains are marked with numbers.
(Reproduced with permission from Ref. [1]. © 1980 Elsevier B. V.)
Figure 3.19 shows an example of a bright-field image of a polycrystalline Al–Cu
alloy with grain boundaries. The darker appearance of certain grains results from
the strong diffraction from their crystallographic planes. When we tilt the specimen
we change the diffraction angle, and the darker grains will become brighter and
the brighter grains will become darker.
Diffraction contrast is very sensitive to specimen tilting. Even a tilt of less than
1◦ can cause the contrast to change from bright to dark. On the other hand, note
that the grains are not always obvious in diffraction contrast. At certain diffraction
angles, only a few grains might satisfy the Bragg conditions and be revealed
(Figure 3.20).
Dark-field is not as commonly used as bright-field imaging. However, the darkfield image may reveal more fine features that are bright when the background
becomes dark. Figure 3.21 shows a comparison between bright- and dark-field
images for the same area in an Al–Fe–Si alloy. The dark-field image (Figure 3.21b)
reveals finer details inside the grains. Interestingly, there are several dark-field
300 nm
Figure 3.20 Bright-field image of fine grained Al–Fe–Si alloy. Only a few grains are visible
at certain specimen orientations.
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100
101
150 nm
(a)
(b)
Figure 3.21 Comparison of bright- and dark-field image of Al–Fe–Si alloy: (a) bright-field
and (b) dark-field images.
images corresponding to a single bright-field image because we can select different
diffraction spots (hkl) in Figure 3.18 to obtain a dark-field image. This is different
from light microscopy in which there is a one-to-one correlation between bright- and
dark-field images. When tilting a specimen to generate a high-intensity diffraction
spot (hkl), we may choose the spot of (hkl), which must exhibit low intensity in this
circumstance, to form a dark-field image. This type of dark-field image is called
the weak-beam dark-field image. Weak-beam imaging is useful for increasing the
resolution of fine features such as dislocations in crystalline materials.
3.3.3
Phase Contrast
Both mass–density and diffraction contrasts are amplitude contrast because they
use only the amplitude change of transmitted electron waves. Chapter 1 mentions
that phase change generates contrast in light microscopy. Similarly, a TEM can also
use the phase difference in electron waves to generate contrast. The phase-contrast
mechanism, however, is much more complicated than that of light microscopy. The
TEM phase contrast produces the highest resolution of lattice and structure images
for crystalline materials. Thus, phase contrast is often referred as to high-resolution
transmission electron microscopy (HRTEM).
Phase contrast must involve at least two electron waves that are different in wave
phase. Thus, we should allow at least two beams (the transmitted beam and a
diffraction beam) to participate in image formation in a TEM. Formation of phase
contrast in a crystalline specimen is illustrated simply in Figure 3.22. A crystalline
specimen with a periodic lattice structure generates a phase difference between
the transmitted and diffracted beams. The objective lens generates an additional
phase difference among the beams. Recombination of transmitted and diffracted
beams will generate an interference pattern with periodic dark–bright changes
on the image plane because of beam interferences, as shown in Figure 3.23.
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3.3 Image Modes
3 Transmission Electron Microscopy
Parallel
−π/2
Diffracted
beam
−π/2
Direct
Objective lens
Reciprocal space
Image
Contrast
Figure 3.22 Phase-contrast formation from a crystalline specimen. Phase difference is generated by crystal diffraction and an objective lens. This results in a phase difference of − π
between the direct and transmitted beams.
5 nm
Figure 3.23 Phase-contrast image of silicon nanowire. (Reproduced with permission of
Ning Wang.)
An interference pattern is a fringe type that reveals the periodic nature of a
crystal.
Theoretical interpretation of phase-contrast images is complicated, particularly
when more than one diffraction spot participates in image formation. The schematic
illustration in Figure 3.22 does not reflect the complexity of phase contrast. The
electron wave theory of phase-contrast formation is explained briefly in the following
section.
3.3.3.1 Theoretical Aspects
The electron wave path of phase contrast in a TEM is illustrated by Figure 3.24. The
properties of electron waves exiting the specimen are represented by an object function,
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102
T(R)
f(r)
F'(R)=F(R) T(R)
r
R
O
r'
f(r')=f(r)∗t(r)
Object plane
Objective
Focal plane
Image plane
Figure 3.24 Two Fourier transformations during formation of a phase-contrast image.
(Reproduced with permission from Ref. [3]. © 1991 John Wiley & Sons Ltd.)
f(r), which includes the distributions of wave amplitude and phase. r is the position vector
from the central optical axis. The object function may be represented as a function in
Eq. (3.3)
f (r) = [1 − s(r)] exp[iφ(r)]
(3.3)
where s(r) represents absorption by the specimen and φ(r) is a phase component of a
wave. For a weakly scattering object (s and φ 1), f(r) may be approximated.
f (r) = 1 − s(r) + iφ(r)
(3.4)
At the back-focal plane of objective lens, the diffraction pattern is considered as the Fourier
transform (FT) of the object function
F(R) = FTf (r)
(3.5)
where R is the position vector of a diffraction spot from the central axis on the focal plane;
a reciprocal vector. The Fourier transform F(R) is defined by the following equation
f (r) exp(2πir × R)dr3
(3.6)
F(R) =
∞
in which r × R is defined.
r × R = xX + yY + zY
(3.7)
X, Y, and Z are the magnitudes of the reciprocal vector R, corresponding to the magnitude
(x, y, and z) of vector r in the real space. Since the electron waves pass the objective lens,
the objective lens can affect the wave characteristics. The effect of the objective lens on the
wave function can be represented by a transfer function, T(R). Thus, the actual wave
function on the back-focal plane becomes the following function.
F (R) = F(R)T(R)
(3.8)
103
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3.3 Image Modes
3 Transmission Electron Microscopy
Wave theory tells us that the wave function of electrons on the image plane (florescent
screen) should be the Fourier transform of F ’ (R). For treatment simplicity, we may ignore
the image magnification and rotation on the image plane. Then, the wave function on
the image plane becomes F ’ (r).
f (r) = FT{F (R)} = FT{F(R)T(R)} = f (r) × t(r)
(3.9)
The results should be read as the convolution product of f(r) by t(r), where t(r) is the
Fourier transform of T(R). The transfer function plays an important role in image
formation. The transfer function can be written as the following equation
T(R) = A(R) exp[−iγ (R)]
(3.10)
where the amplitude factor (A) equals unity when the length of R is less than the objective
aperture radius on the focal plane; otherwise it equals zero. The phase shift (γ ) that
occurs as the waves pass objective lens should be considered. A phase difference occurs
when the wave paths that reach a certain point are different. Spherical aberration causes
phase shift because of the electron wave path difference between the waves near the
central axis and the waves far from the central axis of objective lens. The phase shift
at R in the back-focal plane induced by spherical aberration can be expressed as the
following
γs (R) =
π
C λ3 R4
2 s
(3.11)
Cs is the spherical aberration coefficient. This phase shift by spherical aberration can be
significant for short-wavelength waves such as electrons. Fortunately, this phase shift can
be offset by a phase shift caused by defocusing the image. We can defocus the image and
make the focal point at the distance further from the focal plane (i.e. weaken the lens
power). The phase shift from defocusing the image is a function of the defocus distance
(D) from the focal plane.
γD (R) = −πλDR2
(3.12)
The total phase shift in the transfer function should be the sum of two phase shifts.
1
CS λ2 R4 − DR2
γ = γS + γD = πλ
(3.13)
2
This equation means that we can manipulate the amount of phase shift by defocusing
the image. Formation of a phase-contrast image requires that the wave function on the
image plane satisfies the following condition.
f (r) = 1 + φ(r)
(3.14)
This is possible when the phase shift in the transfer function satisfies the following
equation.
sin γ ∼
= ±1
(3.15)
This condition can be obtained in a defocused condition of the objective lens. As a
result, an image of phase contrast may be interpreted in terms of periodic structures of
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104
Ra
Figure 3.25 The objective aperture opening shown in the back-focal plane. Ra , diameter of
the aperture.
a crystalline solid. Such an image of phase contrast is called the interpretable structure
image.
In order to obtain an interpretable image, the objective aperture opening must be
limited to a level corresponding to the optical resolution limit of the objective lens. In
TEM operation, we can adjust the aperture opening on the image of the back-focal
plane (Figure 3.25). Its dimension is the reciprocal of length (nm−1 ). For example,
the optical resolution limit is about 0.35 nm at an acceleration voltage of 100 kV, and
about 0.25 nm at 200 kV. We should not open the aperture to include diffraction spots
with length of R larger than about 0.35−1 nm−1 for 100 kV and about 0.25−1 nm−1 for
200 kV. An aperture larger than the limit may generate artifacts in the phase-contrast
image.
3.3.3.2 Two-Beam and Multiple-Beam Imaging
We may use the transmitted beam and one diffraction beam fro a crystallographic
plane (hkl) to form a one-dimensional lattice image. This is the simplest way to
obtain a set of fringes that is parallel to the crystallographic plane (hkl). Two-beam
contrast can provide a lattice image as long as the plane spacing is within the
resolution of the TEM. Thus, we may directly measure the plane spacing between
two fringes. Figure 3.26 shows an example of a lattice image of a carbon nanotube
obtained by two-beam phase contrast.
Often, more than two beams are needed to obtain a structure image because
better structure resolution can be obtained with multiple-beam imaging. The phase
contrast, however, for a multiple-beam image is more complicated than for a twobeam case. Compensating the phase shift of spherical aberration with defocusing
is difficult, unless the transmitted beam aligns with a highly symmetrical crystal
axis, for example, the [111] axis of cubic crystals. Although compensating spherical
aberration with defocusing is not possible in some cases, we may still have
interpretable structure resolution when the aperture opening is limited within the
optical resolution.
105
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3.3 Image Modes
3 Transmission Electron Microscopy
Figure 3.26 Two-beam phase contrast of a carbon nanotube at its end portion.
(Reproduced with permission of Ning Wang.)
ZnSe
5 nm
GaP
Figure 3.27 Multiple-beam lattice image of the interface between GaP and ZnSe crystals.
(Reproduced with permission of Ning Wang.)
When two or more diffraction beams participate in image formation, a twodimensional lattice image that exhibits a lattice image of several sets of lattice
planes will be observed, as shown in Figure 3.27. The bright parts of a phasecontrast image generally correspond to small phase shifts in waves as they exit
from a crystal. Thus, they may correspond to structure channels between atomic
planes. Generally, neither a bright nor a dark dot in the image corresponds to an
individual atom. Direct interpretation of a phase-contrast image must be carefully
handled. Often we have to rely on computer simulation based on phase-contrast
theory outlined in the previous section to interpret the structure images formed by
multiple beams.
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106
3.4
Selected-Area Diffraction (SAD)
A diffraction pattern is formed on the back-focal plane of the objective lens
when an electron beam passes through a crystalline specimen in a TEM. In the
diffraction mode, a pattern of SAD can be further enlarged on the screen or
recorded by a camera as illustrated in Figure 3.16. Electron diffraction is not only
useful to generate images of diffraction contrast, but also for crystal structure
analysis, similar to XRD methods. SAD in a TEM, however, shows its special
characteristics compared with XRD, as summarized in Table 3.4. More detailed
SAD characteristics are introduced in the following section.
3.4.1
Selected-Area Diffraction Characteristics
Construction of an image of an SAD pattern in a TEM is illustrated in Figure 3.28.
Constructive diffraction from a lattice plane (hkl) generates an intensity spot on the
screen when the TEM is in the diffraction mode. The diffraction angle in the TEM
is very small (commonly θ < 1◦ ), because the reflecting lattice planes are nearly
parallel to the primary beam. Using the approximation sin θ ≈ θ for a small angle,
we can rewrite Bragg’s Law as the following.
λ = 2dθ
(3.16)
Noting the geometric relation among θ , R, and L demonstrated in Figure 3.28, we
have the following equation
λL = Rd
(3.17)
where L is the camera length of a TEM, the distance between the crystal and
photographic plate of camera. This is not a real physical distance in a TEM
because the magnifying lens changes the geometry of the path between the crystal
and photographic plate. In fact, L is an equivalent camera length for calculating
the spacing of the lattice plane. λL is called as the camera constant of a TEM.
Equation (3.17) is the basic equation for electron diffraction in a TEM. We can
Table 3.4
Comparison between X-ray diffraction and SAD in TEM.
Scattering nature
Wave paths
Diffraction angle θ
Intensity
Precision
X-ray diffraction
SAD in TEM
Scattering by shell electrons
Reflection (XRD)
Transmission (Laue)
0–180◦
Low
High
Scattering by atom nucleus
Transmission
0–2◦
106 –107 times higher
Relatively low
107
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3.4 Selected-Area Diffraction (SAD)
3 Transmission Electron Microscopy
Incident
(hkl)
Specimen
1/λ
2θ
Camera
length (L)
Ewald sphere
(1/λ >> g)
g
R
Figure 3.28
Formation of a diffraction pattern in a TEM.
calculate the spacing of crystallographic planes by measuring R (the distance from
the central spot of the transmitted beam to a diffraction spot) in photographic
film using Eq. (3.17). L can be changed in a TEM: for example, L = 1.0 m is often
selected with 200-kV acceleration voltages. A proper L value allows us to have a
reasonable R range in the image film.
It is important to note the features of diffraction pattern of a single crystal in
TEM: the diffraction pattern represents a reciprocal lattice plane with reciprocal
lattice points that are shown as the diffraction spots, and the reciprocal lattice plane
contains the diffraction of lattice planes belonging to one crystal zone, of which
the axis is parallel to the transmitted beam. These features are well illustrated in
Figure 2.9 in which the zone axis is [001] of a cubic crystal and the reciprocal lattice
plane consists of diffraction spots from lattice planes (hk0).
The Ewald sphere is very useful to explain the formation of diffraction patterns
in a TEM (Figure 2.11). Recall that the short wavelength of high-energy electrons
makes the radius of the Ewald sphere (λ− 1 ) become so large that the spherical
surface is nearly flat compared with the distances between reciprocal lattice points.
On the other hand, a diffraction spot of a crystal with a small dimension in the
vertical direction is not an exact reciprocal lattice point, but an elongated spot along
that direction, as illustrated in Figure 3.29. The reason for spot elongation relates
to diffraction-intensity distribution, which can be fully explained by kinematic
diffraction theory. Without more description of the theory, we may still understand
it by recalling the discussion of crystal size effects on the width of XRD diffraction
peaks in Chapter 2. The width of XRD peaks increases with decreasing crystal size
because a small crystal causes incomplete destructive interference. For the same
reason, the thin crystal of a TEM specimen causes a widened intensity distribution
and thus, the elongated diffraction spots along the vertical direction. Therefore, the
flat surface of the large Ewald sphere can intersect even more diffraction spots on
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108
Intensity
Figure 3.29 Diffraction-pattern formation from a thin foil specimen in a TEM. The surface
of Ewald sphere intersects the elongated diffraction spots. An elongated spot reflects the
diffraction intensity distribution along the transmitted-beam direction.
one reciprocal plane in a TEM, as illustrated in Figure 3.29. Thus, we can see a
diffraction pattern in the TEM, as shown in Figure 3.16.
3.4.2
Single-Crystal Diffraction
To obtain a diffraction pattern as shown in Figure 3.16, we need to use the
selected-area aperture to isolate a single crystal in the image mode, and then switch
to the diffraction mode. Commonly, tilting the specimen is necessary to obtain a
diffraction pattern with high symmetry with respect to its central transmitted spot.
A symmetrical pattern like Figure 3.16 must have a zone axis of the crystal aligned
with the transmitted beam direction, as illustrated in Figure 2.9.
After obtaining a diffraction pattern, we may want to index the pattern in order
to determine the crystal structure or crystal orientation that the pattern represents.
Indexing a pattern means to assign a set of h, k, and l to each diffraction spot in
the pattern. The information can be directly extracted from a pattern that includes
the length of R for each spot and angles between any two R vectors. We can
calculate the interplanar spacing (dhkl ) easily using Eq. (3.17), with knowledge of
the camera constant. Without additional information about the crystal such as
chemical composition or lattice parameters, indexing a pattern could be a difficult
task. However, indexing techniques for simple cases can be demonstrated as
follows.
3.4.2.1 Indexing a Cubic Crystal Pattern
The TEM bright-field image and an SAD pattern of sodium chloride (NaCl) are
shown in Figure 3.30. In the pattern, the central spot of the transmitted beam is
brightest and should be indexed as (0 0 0) of the reciprocal lattice plane. Then, we
can select two spots, for example, m and n in the pattern to measure their R lengths
and angle between them. Here, the R lengths of m and n are measured as 8.92
and 12.6 mm, respectively; and the angle between Rm and Rn is measured as 45◦ .
The indices of the spots can be determined by the following relationship for cubic
crystals such as NaCl. The equation is obtained by combining Eqs. (3.17) and (2.4).
109
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3.4 Selected-Area Diffraction (SAD)
3 Transmission Electron Microscopy
Rm
Rn
(a)
(b)
Figure 3.30 Single crystal of NaCl: (a) bright-field image and (b) selected-area diffraction
pattern. Rm , Rn are the radii of spots m and n, respectively. The transmitted beam direction
is parallel to [001].
R(hkl)
λL(h2 + k2 + l2 )1/2
a
(3.18)
The wavelength of electrons (λ) for 200 kV, which is used to obtain the pattern,
should be 0.00251 nm according to Table 3.2. The diffraction photograph is taken at
the camera length (L) of 1.0 m. Since the lattice parameter of NaCl (a) is 0.563 nm,
we can determine that the Rm matches that of 200 and Rn matches that of 220,
according to Eq. (3.18). Then, we should check whether the angle (Rm Rn ) matches
that between specific planes. The plane angle in a cubic crystal can be obtained
using the following equation.
cos α = hm hn + km kn + lm ln
2
(hm
2 )(h2 + k2 + l2 )
+ k2m + lm
n
n
n
(3.19)
It is not difficult to determine that the measured angle α (45◦ ) matches that of the
angle between (200) and (220) or (200) and (220).
Actually, there is a 180 ◦ ambiguity in the pattern index: an identical pattern is
obtained by rotating 180◦ around the transmitted beam. For convenience, we can
index the spots of the right hand side as (200)(220). After indexing these two spots,
the rest of the spots can be indexed using the rule of vector addition. The crystal
zone axis can be identified by vector algebra.
[uvw] = Rm × Rn
(3.20)
The diffraction pattern in Figure 3.30b should be indexed as illustrated in
Figure 3.31. For the pattern in Figure 3.30, we can quickly determine the crystal
zone axis as [001], according to Eq. (3.20).
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110
22
0
20
0
02
0
22
0
22
0
00
0
02
0
20
0
22
0
Figure 3.31 Indexing the diffraction pattern of NaCl shown in Figure 3.30b.
In certain cases, without knowing the lattice parameter of a crystal, we may still
be able to index the pattern using the relationship between the R ratio and Miller
indices. For example, if the crystal is cubic, the following holds.
2 1/2
)
(h2 + k2m + lm
Rm
= m2
Rn
(hn + k2n + ln2 )1/2
(3.21)
In a cubic system, all the possible R ratios can be tabulated according to hkl pairs. We
may find the match of R ratio for specific hkl pairs of a crystal structure. It should
be remembered that diffraction must obey the structure extinction laws discussed
in Chapter 2. Note that NaCl exhibits a face-centered cubic (FCC) structure for
which the diffraction pattern should not include (hkl) indexes of mixed odd and
even numbers. Thus, there are no diffraction spots for 100, 110, and so on, in
Figure 3.30b. We can use the structure extinction laws to determine whether a cubic
crystal is FCC or body-centered cubic (BCC). According to the structure extinction
laws listed in Table 2.2, the reciprocal lattice of an FCC structure is a BCC type or
vice versa, as shown in Table 3.5.
The crystal orientation with respect to specimen geometry is important information. In Figure 3.30, the NaCl crystal orientation is already revealed by its bright-field
Table 3.5
Relationship between real and reciprocal lattice structure.
Real lattice
Real lattice parameter
Reciprocal lattice
Reciprocal lattice parameter
Simple cubic
a
Simple cubic
a∗ =
FCC
a
BCC
BCC
a
FCC
1
a
2
a∗ =
a
2
a∗ =
a
111
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3.4 Selected-Area Diffraction (SAD)
3 Transmission Electron Microscopy
image, because its cubic shape implies its crystal structure and orientation. In most
cases, crystalline materials do not show the geometrical shape representing their
crystal structure and orientation. Thus, we need to determine the orientation from
single-crystal diffraction patterns.
When paying attention to Figures 3.30a and b, we note that the crystal orientation
of NaCl in the bright-field image does not match that of the diffraction pattern
because the edge of the cube should be perpendicular to R(200) or R(020) in the
diffraction pattern. Figure 3.30 tells us that there is image rotation of the diffraction
pattern with respect to its crystal image. This rotation results from the change
in magnetic field of the electromagnetic lens during switching from the image
mode to the diffraction mode. The reason for this is that the image and the
diffraction pattern are formed in different optical planes in the TEM. The image
has undergone three-stage magnification, but the pattern has only undergone
two-stage magnification.
The rotation angle is a function of TEM magnification, and has to be determined
experimentally. For example, Figure 3.32 shows the rotation angle between a cubic
single crystal and its diffraction pattern. Note that the angle is ϕ + 180◦ , not ϕ,
because each stage of magnification rotates the image by 180◦ . After calibrating the
rotation angle at the given acceleration voltage, magnification, and camera length,
we should be able to determine the orientation of the crystal being examined. Some
modern TEM systems have a function to correct the angle of image rotation automatically. Thus, manual correction is no longer needed when the images are recorded.
3.4.2.2 Identification of Crystal Phases
SAD is particularly useful for identifying the structure of tiny crystals such as
crystalline precipitates. For example, three crystal structures may exist for calcium
phosphates precipitated from supersaturated aqueous solutions: hydroxyapatite
No. B942
image
n
io
ct
ra
iff
D
ϕ
010
N
B
o.
3
94
rn
tte
pa
010
100
100
Figure 3.32
The rotation angle between the image and diffraction pattern of a crystal.
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112
R2
R1
200 nm
(b)
(a)
R2
R1
200 nm
(c)
(d)
Figure 3.33 Calcium phosphate precipitates and their diffraction patterns: (a) image;
and (b) diffraction pattern of octacalcium phosphate crystal; (c) image; and (d) diffraction
pattern of hydroxyapatite crystal. R1 , R2 are vectors.
(HA), octacalcium phosphate (OCP), and dicalcium phosphate dihydrate (DCPD).
Figure 3.33 shows images and their diffraction patterns of precipitation phases
from the solutions. Two diffraction patterns (Figures 3.33b and d) look similar, but
careful examination reveals their differences. Both patterns exhibit a d-spacing of
about 0.68 nm, which is calculated from the R1 length. The crystallographic data
indicate that the (001) d-spacings of OCP and HA are about 0.68 nm, while DCPD
does not have any d-spacing close to 0.68 nm. Thus, the precipitates should only be
either OCP or HA, not DCPD. Note that the R2 length on Figure 3.33b is smaller
than that on Figure 3.33d. The calculated d-spacing is 0.94 nm in Figure 3.32b and
0.82 nm in Figure 3.33d. The crystallographic data show that only OCP exhibits dspacing of 0.94 nm in the (110) plane. Thus, the precipitate in Figure 3.33a is likely
to be OCP. In addition, the angle between R1 R2 should be carefully measured and
compared with crystallographic data. The angles between R1 R2 in Figures 3.33b
and d appear to be 90◦ , but careful measurement reveals the angle in Figure 3.33b
is 90.3◦ , slightly larger 90◦ , while that in Figure 3.33d is exactly 90◦ . In fact, the
angle in Figure 3.33b matches the crystallographic data of OCP, because the planar
113
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3.4 Selected-Area Diffraction (SAD)
3 Transmission Electron Microscopy
(a)
(b)
Figure 3.34 Images of polycrystalline specimen of thallium chloride: (a) SAD ring pattern
and (b) bright-field image in which the dark circle (50 μm diameter) indicates the area selected for diffraction. (Reproduced with permission from Ref. [1]. © 1980 Elsevier B. V.)
angle between OCP (001) and (110) is 90.318◦ . Thus, we can confidently identify
the crystal structure of the precipitate in Figure 3.33a as OCP, which has a triclinic
structure, while the precipitate in Figure 3.33c is identified as HA with a hexagonal
structure.
3.4.3
Multicrystal Diffraction
If an area selected for diffraction contains a large number of single crystals that are
randomly oriented, a ring pattern will be obtained in SAD. Figure 3.34a shows the
SAD ring pattern of a thallium chloride (TlCl) specimen composed of tiny grains.
Formation of SAD ring patterns is similar to that of the X-ray Debye rings shown
in Figure 2.12. The ring formation in the multicrystalline specimen is equivalent
to the rotation of the SAD diffraction of a single crystal around the axis of the
transmitted electron beam, because the grains in a polycrystalline specimen may
show all orientations similar to the pattern produced by single-crystal rotation.
However, rings in an SAD pattern are often broken, as shown in Figure 3.34a,
because it is not likely that a specimen contains grains in all possible orientations.
The SAD ring pattern can also be formed when the selected-area aperture includes
many individual tiny crystals.
3.4.4
Kikuchi Lines
Kikuchi lines are pairs of parallel lines consisting of one bright and one dark line
in the diffraction mode as shown in Figure 3.35. Kikuchi lines are named after the
Japanese scientist, Kikuchi, who discovered them in 1928. Kikuchi lines appear
when the selected area for diffraction is moved to a thicker section in the specimen
where the diffraction spots become weaker, or even disappear.
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114
B
B′
A′
A
Figure 3.35 Kikuchi lines (pairs of light and dark lines) marked AA and BB in an aluminum specimen. (Reproduced with permission from Ref. [4]. © 1988 Taylor & Francis
Group Ltd.)
Kikuchi lines result from inelastic scattering of electrons in specimens. Generally,
an electron scatters elastically when it interacts with an atomic nucleus. The mass
of a nucleus is much larger than that of an electron. Thus, their interaction is
similar to a ball hitting a wall where the ball bounces without energy loss. However,
when the electron interacts with an electron in an atomic shell, energy will transfer
between the two electrons during collision, which is referred as to inelastic scattering
of electrons. The intensity of inelastically scattered electrons varies with the angle
between the incident ray and scattering direction. A consequence of inelastic
scattering is that the primary incident rays of electrons scatter from a location in a
specimen as a cone of electron rays to all directions in a specimen, as illustrated in
Figure 3.36. The cone of electron rays becomes a secondary electron source with a
maximum intensity in the direction of the primary beam. The intensity decreases
with increasing angle between the scattering and the primary ray direction. The
formation of Kikuchi lines can be explained by the nature of this secondary electron
source radiation in a specimen.
Io
I
β
Iα
α I
α
(a)
Iβ
β
α
(b)
Figure 3.36 Inelastic scattering in a specimen: (a) cone of electron radiation is generated by inelastic scattering and (b) intensity of inelastic scattering decreases with angle between the primary beam direction and the scattered ray. (Reproduced with permission from
Ref. [1]. © 1980 Elsevier B. V.)
115
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3.4 Selected-Area Diffraction (SAD)
3 Transmission Electron Microscopy
P
hkl
I2
I1
k2
I2(1-c)
k2′ k1
k1′
I1c
I1(1-c)
I 2c
I
c(I1-I2)
c(I1-I2)
K2
K1
View
screen
Figure 3.37 Kikuchi-line formation by inelastic scattering of electrons at point P in a single crystal. The lower diagram illustrates the intensity of light on the view screen, which is
affected by the inelastic scattering at P.
Figure 3.37 illustrates inelastic scattering at point P between two (hkl) planes
inside a crystalline specimen. Inelastic scattering at P generates a cone of rays as
a secondary source of incident electrons that form the background intensity, as
shown in the lower part of Figure 3.37. Since the electron rays from this secondary
source P are incident in all directions, there must be rays (represented by vectors
k1 and k2 ) with the incident angle (θ ) satisfying the Bragg condition for plane (hkl)
and (hkl). These rays k1 and k2 generate constructive diffraction on the back-focal
planes at K 1 and K 2 . The intensity of k1 is larger than that of k2 because k2 is more
inclined from the primary beam direction than k1 . As shown in Figure 3.37, the
reflected ray of k1 (k1 ) is parallel to k2 and the reflected ray of k2 (k3 ) is parallel to
k1 . We can determine the total intensity at K 1 and K 2 as follows
IK1 = I1 (1 − c) + I2 c = I1 − c(I1 − I2 )
IK2 = I2 (1 − c) + I1 c = I2 + c(I1 − I2 )
(3.22)
I1 and I2 are the background intensity at K 1 and K 2 , respectively, and c is the ratio
of the reflected intensity to the incident intensity. Thus, contrast will be generated
at K 1 and K 2 on the inelastic background; thus, a dark image will appear at K 1 and
a bright image will appear at K 2 , as illustrated in Figure 3.37.
Figures 3.36 and 3.37 only illustrate the situation in the figure plane. In fact,
inelastic scattering generates a cone of electron rays incident in front of and behind
the figure plane. Consequently, those rays also generate diffraction spots in the
back-focal plane. Thus, diffraction on the back-focal plane is no longer a single
spot, but a locus of diffraction spots. This means that there should be a dark line
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116
Figure 3.38 Kikuchi pattern of a silicon foil symmetrically oriented along the [111] zone.
The pattern reveals sixfold symmetry. (Reproduced with permission from Ref. [5]. © 1997
Wiley-VCH.)
and a bright line perpendicular to the figure plane of Figure 3.37 at positions K 1
and K 2 , respectively.
Kikuchi lines can be used to guide specimen tilting. For example, if the (hkl) plane
is perfectly parallel to the radiation cone at P, then I1 = I2 . The difference between
the dark and bright lines will disappear. Figure 3.38 shows the Kikuchi pattern of
silicon crystal with perfect alignment of the electron beam along the crystal [111]
zone axis. Note that the area between two lines is darker than the background in
the symmetric Kikuchi lines as shown in Figure 3.38. In such patterns, a lattice
plane (hkl) parallel to the Kikuchi lines must be located at the center between the
lines. We can use the symmetrical patterns of Kikuchi lines centered at a point to
obtain perfect alignment of the incident beam with a crystal zone axis.
3.5
Images of Crystal Defects
Understanding TEM images is often not as straightforward a task as a lightmicroscope image, except for images with mass–density contrast. For understanding images with diffraction contrast, we need more extensive knowledge of electron
diffraction in crystalline solids. This section interprets several typical images of
crystalline solids in diffraction-contrast conditions.
3.5.1
Wedge Fringe
A fringe pattern (a set of parallel dark and bright lines) appears near the edge
of thin foil specimens, as shown in Figure 3.39, or near grain boundaries of a
polycrystalline specimen, as shown in Figure 3.40. The wedge fringe is generated
in a crystalline solid with a continuous change of thickness that forms a wedge
117
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3.5 Images of Crystal Defects
3 Transmission Electron Microscopy
(a)
(b)
Figure 3.39 Wedge fringes at an edge of aluminum foil: (a) bright-field image (20 000×
magnification) and (b) schematic illustration of the wedge shape of a foil edge. (Reproduced with permission from Ref. [1]. © 1980 Elsevier B. V.)
1 μm
Grain A
1
(a)
Grain B
2
(b)
Figure 3.40 Wedge fringes at a grain boundary: (a) bright-field image and (b) schematic
illustration of grain-boundary orientation in a specimen that generates the fringes in the
bright-field image. (Reproduced with permission from Ref. [1]. © 1980 Elsevier B. V.)
shape. Full understanding of a wedge fringe requires knowledge of kinematic and
dynamic theories of electron diffraction, which is beyond the scope of this book.
Without the details of these theories, a simple interpretation of the wedge fringe is
provided as follows.
Electron diffraction in the TEM often does not satisfy the exact conditions of
Bragg’s Law. This relaxation of Bragg’s Law in a TEM is illustrated in Figure 3.29, in
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118
2θ
k
k0
s
g
Figure 3.41 Deviation from Bragg’s Law diffraction illustrated by the Ewald sphere method.
The deviation from exact Bragg conditions is represented by vector s in reciprocal space.
k0 is the primary beam vector, k is the scattering beam vector and g is a reciprocal lattice
vector.
which the reciprocal lattice points are elongated in the transmitted beam direction
due to the small thickness of a TEM specimen. The deviation from the exact Bragg
conditions can be represented by a deviation vector (s) in reciprocal space, as shown
in Figure 3.41. The kinematic theory of diffraction indicates that the diffraction
intensity periodically change with thickness of specimen (t)
Id ∝
sin π st
πs
2
(3.23)
s is the component of vector s parallel to the transmission vector ko as illustrated in
Figure 3.41. For a given crystal orientation, s is a constant in Eq. (3.23), and thus,
the intensity of the diffracted beam must oscillate between zero and a maximum
with thickness increase, as illustrated in Figure 3.42. In a wedge-shaped crystal, we
see a bright fringe where t = ns− 1 and a dark fringe where t = n + (2s)−1 , in which
n is an integer.
The wedge-fringe pattern is also seen at stacking faults. Stacking faults are a
special type of planar defect in FCC crystals caused by disorder in the stacking
sequence on the {111} planes. There is an interruption of the lattice structure at the
fault plane. The stacking-fault plane separates FCC crystal into two parts. Thus, the
stacking-fault plane is very similar to a grain-boundary plane. Figure 3.43 shows
a typical image of stacking faults that exhibit fringe patterns similar to a wedge
fringe. The ends of fringes are the locations of partial dislocations separating a
stacking fault from the rest of the crystal. Figure 3.44 schematically illustrates
the formation of a wedge fringe when the stacking-fault plane is inclined to the
transmitted beam. The electron beam is intersected by the fault plane. The result
will be generation of fringes in the diffraction contrast image.
119
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3.5 Images of Crystal Defects
3 Transmission Electron Microscopy
Incident electron wave
Wedge-shaped
crystal
t
1/s
2/s
Id
1/s
2/s
t
Figure 3.42 Electron-intensity oscillation in the thickness direction of a specimen. A
wedge-shaped crystal generates dark and bright fringes in the image because of the continuous change in thickness of the wedge.
B
A
0.5 μm
Figure 3.43 Bright-field image of stacking faults in a Co–Ni–Cr–Fe alloy. Partial dislocations are visible at A, but not at B. (Reproduced with permission from Ref. [1]. © 1980
Elsevier B. V.)
3.5.2
Bending Contours
Dark bands in the background are often seen in images acquired in the diffraction
contrast mode, as shown in Figure 3.45. The bands are called bending contours and
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120
t
2
1
Stacking Fault
A
B
C
A
B
C
A
C
A
B
C
A
B
t
Figure 3.44 Wedge-fringe formation at a stacking fault. The face of stacking fault divides
a face-centered cubic crystal into parts 1 and 2. A transmitted beam column crossing the
fault is similar to that crossing a grain boundary, as shown in Figure 3.39b.
Figure 3.45 Bright-field image of bending contours. (Reproduced with permission of
Ning Wang.)
commonly are diffuse and curved. The bending contours result from the distorting
or bending of a specimen foil. In the bent portion, the lattice plane is rotated with
respect to the transmitted beam direction. At a certain location, such a rotated
lattice plane may satisfy Bragg conditions exactly. Thus, a dark band appears in
the bright-field image at such a location because the diffraction beams removed a
significant portion of electrons from the transmitted beam. The bending contours
121
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3.5 Images of Crystal Defects
3 Transmission Electron Microscopy
2θ
r
θ
hkl
hkl
2θ
hkl Fringe
hkl Fringe
hkl
hkl
hkl Fringe
hkl Fringe
Figure 3.46 Formation of a pair of bending contours. (Reproduced with permission from
Ref. [1]. © 1980 Elsevier B. V.)
often appear as pairs. The pairing of bending contours occurs as the specimen
foil is bent symmetrically with respect to the transmitted beam, as shown in
Figure 3.46. In a foil with symmetric bending, there are two locations where lattice
planes (hkl) and (hkl) satisfy the exact Bragg conditions. Thus, we will see the
two dark bands appear simultaneously in a bright-field image. Often, we can tilt a
specimen to check whether the dark bands on the bright background are bending
contours. Bending contours are sensitive to specimen tilting. They move quickly
on the screen during tilting, but wedge fringes do not move quickly as they are less
sensitive to tilting.
3.5.3
Dislocations
One of the great advantages of a TEM is its ability to reveal dislocations, which are
crystal line defects. Figure 3.47 shows typical images of dislocations in bright-field
micrographs. The dislocations appear as fine, dark lines in the bright-field images
and as bright lines in the dark-field images. The configurations of dislocations
vary with specimens: they may be randomly distributed (Figure 3.47a), lined up
(Figure 3.47b) and even form tangled cell walls (Figure 3.47c).
The formation of dislocation images can be graphically explained using an
example of edge dislocations (Figure 3.48). An edge dislocation in a crystal
generates local lattice distortion, as schematically shown in Figure 3.48. A portion
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122
0.5 µm
1 µm
(b)
(a)
1 µm
(c)
Figure 3.47 Bright-field images of dislocations: (a) in a Al–Zn–Mg alloys with 3% tension
strain; (b) lining up in a Ni–Mo alloy; and (c) dislocation cell structure in pure Ni. (Reproduced with permission from Ref. [1]. © 1980 Elsevier B. V.)
of distorted lattice planes is severely bent near the dislocation core. When the bent
portion of the planes satisfies the Bragg conditions, a significant proportion of
electrons in the transmitted beam will be deflected into the diffraction direction
and the diffraction intensity immediately increases at such a portion of the lattice
plane. Thus, in the bright-field image, a dark image forms at point a that is near the
dislocation core located at b, as illustrated in Figure 3.48. Since the dislocation is a
line defect, we should see a dark line that is extended into the plane of Figure 3.48.
A screw dislocation also has a dark line image for the same reason as an edge
dislocation. A screw dislocation also bends lattice planes near its core to generate a
plane orientation that satisfies the Bragg conditions locally. The difference between
an edge and screw dislocation is the bending direction, which is determined by the
Burger’s vector of dislocations.
By understanding the formation of dislocation line images, the formation of the
dislocation pattern in Figure 3.47b can be interpreted by a schematic illustration
(Figure 3.49). Figure 3.47b shows a line-up of dislocations. The lined-up dislocations
lie in a crystal slip plane that is inclined to the transmitted beam. The slip plane
123
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3.5 Images of Crystal Defects
3 Transmission Electron Microscopy
is cut off at the upper and lower surfaces of a thin foil specimen. Thus, only a
short section of dislocations in the slip plane can be seen on the image screen of
a TEM.
BF Intensity
Dislocation core
1
0
ab
Figure 3.48 Formation of a dislocation image by deflection of transmitted electrons due to
local diffraction near the core of an edge dislocation. BF, bright-field.
Electron beam
Succession of
dislocations
Slip plane
(a)
Image plane
(b)
Figure 3.49 Configuration of dislocations in a thin foil when they line up in a single slip
plane: (a) orientation relation between primary electron beam and dislocations in a crystal
plane and (b) the dislocation images projected on a TEM image plane.
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124
Questions
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
Generally, the wavelength of electrons
(λ) and the acceleration voltage (V o )
has a relationship given by: λ ∝ 1/ Vo . Do the values in Table 3.2 satisfy
the relationship exactly? Show the relationships between λ and V o in Table
3.2 and compare them with values obtained from this relationship.
The resolution of a TEM is limited by diffraction (Rd ) as discussed in
Chapter 1, Eq. (1.3)), and by the spherical aberration which is expressed
as: Rsph = Cs α 3 , where Cs is the spherical aberration coefficient and α is the
half-angle of the cone of light entering the objective lens. The TEM resolution
is the quadratic sum of the diffraction resolution
and spherical aberration
resolution, given by the expression: (R = R2d + R2sph ). The minimum R is
obtained when Rd ∼
= Rsph . Estimate the optimum value of α and resolution
limit of TEM at 100–200 kV. Cs ∼
= 1 mm for an electromagnetic objective
lens.
Specimen preparation is a key factor for TEM examinations. How will
you prepare specimens of metal, ceramics, polymer and nanoparticles,
respectively?
Explain how is it possible to increase the contrast of a mass–density image.
Can we obtain a mass–density image of metal specimen? Can we obtain
diffraction contrast in a polymer specimen?
Note that both the mass–density and the diffraction contrast require only
a transmitted beam to pass through the objective aperture. How can you
know you have diffraction contrast without checking selected-area diffraction
(SAD)?
Can you get a dark-field image for mass–density contrast? What is the main
difference of dark-field images between light microscopy and TEM?
Adjusting the objective aperture is an important step to obtain phase contrast
in TEM. Compare the differences in objective aperture operation between
diffraction contrast and phase contrast.
Sketch the diffraction patterns of single crystals in a TEM for (i) a facecentered cubic (FCC) crystal with transmitted beam direction (B) parallel to
[001] and (ii) a body-centered cubic (BCC) crystal with B = [001].
Is a zone axis of a single-crystal diffraction pattern exactly parallel to the
transmitted beam? Explain your answer graphically.
What kind of diffraction patterns should you expect if an SAD aperture
includes a large number of grains in a polycrystalline specimen? Why?
You are asked to obtain maximum contrast between one grain and its
neighbors. Which orientation of crystalline specimen do you wish to obtain?
Illustrate your answer with a pattern of single-crystal diffraction.
Why does formation of Kikuchi lines require a relatively thick specimen?
You have been told that thickness fringe and bending contours can be
distinguished. Explain how.
The reason we see a dislocation is that it bends a crystal plane near its core
region. Indicate a case where we may not be able to see the dislocation
125
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3.5 Images of Crystal Defects
3 Transmission Electron Microscopy
in diffraction contrast under a two-beam condition (a two-beam condition
refers to a crystal orientation in which the intensity of one diffraction spot is
much higher than those of the other diffraction spots). Indicate the answer
either graphically or using the relation of vectors g (the normal of planes
which generate the diffraction beam) and b (Burgers vector of dislocation).
References
1. von Heimandahl, M. (1980) Electron
2.
3.
4.
5.
Microscopy of Materials, Academic Press,
New York.
Shindo, D. and Oikawa, T. (2002) Analytical Electron Microscopy for Materials
Science, Springer-Verlag, Tokyo.
Eberhart, J.P. (1991) Structural and
Chemical Analysis of Materials, John
Wiley & Sons, Ltd, Chichester.
Goodhew, P.J. and Humphreys, F.J.
(1988) Electron Microscopy and Analysis,
2nd edn, Taylor & Francis, London.
Amelinckx, S.,
van Dyck, D., van Landuyt, J., and
van Tendeloo, G. (1997) Handbook of
Microscopy: Applications in Materials Science, Solid-State Physics and Chemistry,
Wiley-VCH Verlag GmbH, Weinheim.
Further Reading
Flegler, S.L., Heckman, J.W. Jr., and
Klomparens, K.L. (1993) Scanning and
Transmission Electron Microscopy, an Introduction, W.H. Freeman, New York.
Spence, J.C.H. (1988) Experimental HighResolution Electron Microscopy, 2nd edn,
Oxford University Press, Oxford.
Horiuchi, S. (1994) Fundamentals of HighResolution Transmission Electron Microscopy,
North Holland, Amsterdam.
Fultz, B. and Howe, J.M. (2001) Transmission
Electron Microscopy and Diffractometry of
Materials, Springer, New York.
Brandon, D. and Kaplan, W.D. (1999) Microstructural Characterization of Materials,
John Wiley & Sons, Ltd, Chichester.
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126
4
Scanning Electron Microscopy
The scanning electron microscope (SEM) is the most widely used type of electron
microscope. It examines microscopic structure by scanning the surface of materials,
similar to scanning confocal microscopes but with much higher resolution and
much greater depth of field. An SEM image is formed by a focused electron beam
that scans over the surface area of a specimen; it is not formed by instantaneous
illumination of a whole field as for a TEM (transmission electron microscope).
Perhaps the most important feature of an SEM is the three-dimensional appearance
of its images because of its large depth of field. For example, the depth of field
can reach the order of tens of micrometers at 103 × magnification and the order
of micrometers at 104 × magnification. An SEM is relatively easily operated and
maintained, compared with a TEM. In addition, an SEM system enables us
to obtain chemical information from a specimen by using various techniques,
including by equipping the X-ray energy-dispersive spectrometer (EDS). EDS is
separately introduced as a technique for chemical analysis in Chapter 6. This
chapter introduces the basic working principles and features of an SEM for
microstructural and surface morphology examination.
4.1
Instrumentation
4.1.1
Optical Arrangement
A SEM consists of an electron gun and a series of electromagnetic lenses and
apertures, as illustrated in Figure 4.1, similar to TEM systems. In an SEM,
however, the electron beam emitted from an electron gun is condensed to a fine
probe for surface scanning. The electron gun for generating an electron beam is
the same as in a TEM; either thermionic or field emission type guns that were
introduced in Chapter 3 are used. Advanced SEM systems use a field emission
gun because of its high beam brightness. Beam brightness plays an even more
important role in imaging quality in an SEM than in a TEM. The relationship
between the brightness and resolution will be discussed in Section 4.1.3. The
acceleration voltage for generating an electron beam is in the range 1–40 kV, which
is about 1 order of magnitude less than that for a TEM.
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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127
4 Scanning Electron Microscopy
Electron gun
1st Condenser
Spray aperture
Scan coils
2nd Condenser
Magnification
control
Objective lens
Scan
generator
Final lens aperture
Detector
Amp
Display
screen
Specimen
To
vacuum
pumps
Figure 4.1 Structure of a scanning electron microscope (SEM). (Reproduced with
kind permission of Springer Science and Business Media from Ref. [1]. © 1992
Springer Science.)
An SEM optical path goes through several electromagnetic lenses, including
condenser lenses and one objective lens, as shown in Figure 4.1. The electromagnetic lenses in an SEM are for electron probe formation, not for image formation
directly as in a TEM. The two condenser lenses reduce the crossover diameter of the
electron beam; then, the objective lens focuses the electron beam as a probe with
a diameter on the nanometer scale. The objective lens should be considered as the
third condenser lens in the SEM because it functions more like a condenser than
an objective lens. The reason for this is that the objective lens in SEM demagnifies
the cross section of the electron beam; thus, it functions very differently from
the objective lens in a TEM, which magnifies the electron beam. The SEM lens
system demagnifies the electron beam by about 10,000× for a thermionic source
and 10–100× for a field emission source.
Probe scanning is operated by a beam-deflection system incorporated within the
objective lens in an SEM. The deflection system moves the probe over the specimen
surface along a line and then displaces the probe to a position on the next line for
scanning, so that a rectangular raster is generated on the specimen surface. The
signal electrons emitted from the specimen are collected by a detector, amplified,
and used to reconstruct an image, according to a one-to-one correlation between
scanning points on the specimen and picture points on a screen of a cathode ray
tube (CRT) or liquid crystal display. The deflection system of the electron probe is
controlled by two pairs of electromagnetic coils (scan coils). The first pair of coils
bends the beam off the optical axis of the microscope. The second pair of coils
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128
bends the beam back onto the axis at the pivot point of a scan. The apertures in an
SEM, as shown in Figure 4.1, are mainly used for limiting the divergence of the
electron beam in its optical path.
The magnification of an SEM is determined by the ratio of the linear size of the
display screen to the linear size of the specimen area being scanned, not as in a
TEM where magnification is determined by the power of the objective lens. The
size of the scanned rectangular area (raster) can be varied over a tremendously
wide range. Thus, an SEM is able to provide image magnification from about
20× to greater than 100,000×. For low-magnification imaging, an SEM is often
more favorable than a light microscope (LM) because of the large depth of field
in SEM. A comparison between LMs and SEMs is demonstrated by the images
shown in Figure 4.2. Both the LM and SEM images in Figure 4.2 reveal the
plane configuration of an integrated circuit, but the SEM image (Figure 4.2b) also
reveals the out-of-plane details because of its three-dimensional appearance. The
resolution of an SEM is controlled by the size of the electron probe scanning the
specimen. Recalling that the effective magnification limit as discussed in Chapter 1
is determined by resolution of the microscope, for a probe size of 10 nm, SEM
systems can generate effective magnifications of 20,000×.
4.1.2
Signal Detection
The electron signals from each pixel of the raster are collected by a detector in
order to generate a corresponding point-to-point image on a display screen. To
understand signal detection, knowledge of electron signal types that are useful in
an SEM is necessary: backscattered electrons (BSEs) and secondary electrons (SEs).
20 kV
(a)
X200
100 μm
(b)
Figure 4.2 Comparison of images taken in: (a) a light microscope and (b) an SEM. An
SEM image (b) is able to provide the 3D appearance of an integrated circuit, while revealing the same inplane details as the light-microscopic image (a).
129
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4.1 Instrumentation
4 Scanning Electron Microscopy
When high-energy electrons strike a specimen, they produce either elastic
or inelastic scattering. Elastic scattering produces the BSEs, which are incident
electrons scattered by atoms in the specimen. Inelastic scattering produces SEs,
which are electrons ejected from atoms in the specimen. BSEs are typically deflected
from the specimen at large angles and with little energy loss; they typically retain
60–80% of the energy of incident electrons. In contrast, SEs are typically deflected
at small angles and show much lower energy compared with incident electrons.
During inelastic scattering, an incident electron transfers kinetic energy to an
electron in a specimen atom. Any electron in the specimen atom with sufficient
kinetic energy will leave its orbital to become a SE. The SE energy is usually in
the range of about 3–5 eV. In terms of usefulness, SEs are the primary signals for
achieving topographic contrast, while BSEs are useful for formation of elemental
composition contrast.
4.1.2.1 Detector
A commonly used detector in an SEM is the Everhart–Thornley (E–T) detector,
as illustrated in Figure 4.3. The SEs travel with large deflection angles toward
the detector, while BSEs travel directly toward the detector. The Faraday cage in
the front of the detector is either positively or negatively charged (250 or −50 V),
depending on signal selection. When given a positive charge, the detector attracts
signal electrons, particularly, SEs. When given a negative charge, it can screen
out SEs with energy less than 50 eV. The key element of the E–T detector is the
scintillator, a disk of about 8–20 mm in diameter. The scintillator converts signal
electrons into photons by accelerating the electrons with +12 kV and striking
them onto a disk. The photons then travel through a light guide and enter the
photomultiplier tube for signal gain (up to ∼106 ×). The photomultiplier output is
further amplified for display on a display screen.
Beam
+ 12 kV
F
PM
LG
S
B
B
B
B
B
SE
B
Specimen
− 50 V to
+ 250 V
Figure 4.3 Signal collection by the Everhart–Thornley detector. B, backscattered electron
trajectory; SE, secondary electron trajectory; F, Faraday cage; S, scintillator; LG, light guide;
PM, photomultiplier tube. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 1992 Springer Science.)
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130
Images in the modern SEM are recorded digitally. That is, the intensity of signal
electrons for each pixel is digitized and saved on computer as a digital file for
each scan. An advantage of digital imaging is the ability to generate an image by
averaging multiple scans for the same area. Such a frame-averaging method can
effectively reduce background noise in imaging.
4.1.3
Probe Size and Current
The resolution of SEM imaging is determined by the cross-sectional diameter of
the scanning probe. Thus, the size of the probe limits the size of features on the
specimen surface to be resolved. To obtain high resolution, we should know how
to minimize probe size. The probe diameter is approximately expressed as dp
dp =
4ip
1/2
(4.1)
βπ2 αf 2
ip is the probe current, β is the beam brightness, which is controlled by the electron
source, and α f is the convergence angle of the probe, which is determined by the
final aperture diameter and the distance between aperture and specimen surfaces
(called the working distance) as illustrated in Figure 4.4.
The brightness of electron illumination or beam brightness (β) depends on the
type of electron gun used. As indicated in Table 3.3, a field emission gun is
1000× brighter than a tungsten thermionic gun and 100× brighter than a LaB6
thermionic gun. Thus, the field emission gun has been widely used in advanced
SEM systems. In any case, regardless of gun type, the brightness is proportional to
αf
Final
aperture
ip
Working
distance
dp
Specimen
Figure 4.4 Relationship between the probe diameter, convergence angle, and working
distance.
131
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4.1 Instrumentation
4 Scanning Electron Microscopy
the acceleration voltage (V o ) of the gun
β ∝ e Vo
(4.2)
where e is the charge of an electron. To obtain a minimal probe size, we should
increase the brightness as well as the convergence angle, as indicated in Eq. (4.1).
On the other hand, a large α f likely introduces other optical problems, particularly
spherical aberration. Thus, α f must be optimized, not simply increased. With an
optimized α f (and neglecting chromatic aberration), the minimum probe size is
approximated as dmin
3/8
ip
dmin = KCs1/4
(4.3)
+ λ2
β
K is a constant close to unity, Cs is the spherical aberration coefficient, and
λ is the wavelength of the electrons. Equation (4.3) simply tells us that we
should decrease wavelength and spherical aberration and increase the brightness
of electron illumination to obtain the minimal probe size. The importance of
electron gun type in determining SEM resolution becomes obvious because there
are significant differences in their brightnesses. Figure 4.5 shows the difference
between probe sizes when different guns are used. The wavelength effects on probe
size can be considered as the acceleration voltage effect, because of the relationship
between the voltage and the wavelength (Table 3.2). Figure 4.6 shows the difference
in probe size when different acceleration voltages are used.
Even though reducing the probe size is necessary, the reduction of probe size
alone is not sufficient to obtain a high-resolution image in an SEM. For obtaining
a high-resolution image, there must be sufficient signal electrons generated by
the probe for each pixel of an image in order to distinguish the signals from the
1000
Probe diameter (nm)
10 kV
100
Tungsten
LaB6
10
FE Pinhole
FE Immersion
1
0.001
0.01
0.1
Probe current (nA)
1
10
Figure 4.5 Probe size is determined by the type of the electron gun and probe current.
(Reproduced with kind permission of Springer Science and Business Media from Ref. [1].
© 1992 Springer Science.)
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132
1000
Probe diameter (nm)
Tungsten
100
30 kV
10 kV
LaB6
10
1
1
10
100
Probe current (nA)
1000
Figure 4.6 Probe size determined by the acceleration voltage of the electron gun. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 1992
Springer Science.)
background noise of electrons. The signal electrons are proportional to the number
of incident electrons in the probe. In other words, the probe current must be larger
than a minimum value so that microscopic features of the specimen are visible in
the SEM image.
The relationship between the probe current and image visibility can be understood by analyzing the basic requirements that an image will not be obscured by
background noise. Background noise in an SEM system is generated by fluctuation
of the electron beam current and signal amplification in the detector, and cannot
be totally eliminated.
Figure 4.7 schematically shows the characteristics of signals and noise. The image
signals from a specimen can be represented by a curved line varying with scan
position. The background noise is represented by a vertical fluctuation imposed on
Signal intensity
Noise
ΔS
Scan position
Figure 4.7 Signals and background noise produced when scanning a specimen.
133
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4.1 Instrumentation
4 Scanning Electron Microscopy
the curved line. The Rose visibility criterion states that, to distinguish two objects
from the background noise, the change in signal (S) due to the object contrast
must be five times larger than the noise level (N).
S > 5N
(4.4)
The noise level can be expressed as the standard deviation of signals. Suppose that
a signal S consists of n counts at the detector; its noise level is then considered
to be the square root of its mean n value. Thus, we can rewrite the Rose visibility
criterion.
S > 5n1/2
(4.5)
Recalling the definition of contrast (C) (Eq. (1.6)), we can express the criterion for
signal counts.
C=
5n1/2
5n1/2
S
>
=
S
S
n
n>
2
5
C
Thus,
(4.6)
In an SEM, the number of counts is the number of signal electrons being detected.
The relationship between counts and current of signal electrons (is ) for the dwell
time of probe (τ ) on an object is calculated by the following expression
ne
(4.7)
τ
Here, is is not equal to the probe current (ip ) but proportional to it. By converting
the criterion for electron counts to the probe current, we have the minimum
requirement of probe current
is =
25e
(4.8)
εC2 τ
ε is the proportionality factor between ip and is . This minimum requirement, or
threshold value, for probe current is necessary to observe a certain level of object
contrast in an SEM. The dwell time of the probe (τ ) is often expressed in terms of
the time required for scanning one frame
t
(4.9)
τ= f
nPE
ip >
tf is the time required to scan one frame and nPE is number of pixels in one frame.
Thus, we should increase the frame time by reducing the scanning speed in order
to satisfy the probe current criterion. Figure 4.8 shows the relationship between
the contrast, frame time, and the minimum probe current required.
In summary, the resolution of an SEM is determined by the probe size (Eq.
(4.3)) and the probe current (Eq. (4.8)). The important points to note are that
the minimum probe size and the maximum probe current cannot be obtained
simultaneously, and a compromise between the probe size and the probe current
must be made when we try to obtain a high-resolution image in SEM.
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134
100
10−13
10−12
10−11
10
Contrast (%)
10−10
10−9
10−8
1
10−7
10−6AMPS
0.1
1
10
100
Frame time (s)
1000
Figure 4.8 Image-contrast variation with probe current and frame time. (Reproduced with
kind permission of Springer Science and Business Media from Ref. [1]. © 1992 Springer
Science.)
4.2
Contrast Formation
There are two types of contrast in SEM images: topographic and compositional.
The SEs are the primary source for surface topographic images, while BSEs are
mainly used for compositional images. Knowledge about the interaction between
the high-energy electron probe and the specimen is necessary for understanding
these mechanisms of contrast formation.
4.2.1
Electron–Specimen Interactions
When high-energy electrons strike a specimen, the electrons are scattered by atoms
of the specimen, as described briefly in Section 4.1. Electron scattering results in
a change of direction of travel of electrons under the specimen surface. Electron
trajectories during scattering in a specimen are schematically shown in Figure 4.9.
As shown in Figure 4.9, the interaction between electrons and specimen atoms
occurs within a certain volume under the specimen surface.
Both SEs and BSEs generated by scattering are used as signal sources for forming
SEM images. However, SEs and BSEs, which are collected by a detector, escape
from different locations in the specimen. Figure 4.10 illustrates the interaction zone
where electrons scatter under the specimen surface. The zone is usually described
as pear-shaped, and its size increases with the energy of incident electrons in
the probe. Besides SEs and BSEs, characteristic X-rays are also produced in the
135
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4.2 Contrast Formation
4 Scanning Electron Microscopy
0.5 μm
Figure 4.9 Monte Carlo electron trajectory simulation of an electron beam interaction with
iron Eo = 20 keV. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 1992 Springer Science.)
Electron
probe
Specimen surface
dp
5–50 nm
Secondary electrons
50–300 nm
Backscattered electrons
Characteristic X-rays
BSE spatial resolution
Figure 4.10
surface.
The interaction zone of electrons and specimen atoms below a specimen
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136
interaction zone, and these are useful for chemical analysis, which is discussed in
Chapter 6.
As mentioned previously, SEs are the products of inelastic scattering, and they
have an energy level of several electron volts. In the interaction zone, SEs can
escape only from a volume near the specimen surface with a depth of 5–50 nm,
even though they are generated in the whole pear-shaped zone. In contrast, BSEs
are the products of elastic scattering, and they have an energy level close to that
of incident electrons. Their high energy enables them to escape from a much
deeper level in the interaction zone, from depths of about 50–300 nm. The lateral
spatial resolution of an SEM image is affected by the size of the volume from
where the signal electrons escape. We can expect, as shown in Figure 4.10 that an
image formed by SEs should have a better spatial resolution than that formed by
BSEs. The characteristics of images formed by SEs and BSEs are discussed in the
following sections.
4.2.2
Topographic Contrast
Topographic contrast in an SEM refers to variation in signal levels that corresponds
to variation in geometric features on the specimen surface. Topographic contrast is
the primary source of contrast in an SEM image. An SEM image with topographic
contrast often has the stereoscopic appearance of a rough specimen surface.
Topographic contrast occurs because signal electrons arise from two effects: the
trajectory effect and the electron number effect. The trajectory effect arises from
variations in how the specimen surface is oriented with respect to the detector.
As schematically shown in Figure 4.11, the electrons emitted from the specimen
surfaces facing the detector will be collected abundantly, and corresponding sites
in the image will appear bright. The electrons emitted from the surfaces not facing
the detector will reach the detector with difficulty, and thus corresponding sites
Beam
+ 250 V
a
b
c
Line of sight
d
Figure 4.11 Generation of topographic contrast: (a) the trajectory effect, which arises
from the orientation of surface with respect
to the detector in an SEM, is similar to: (b)
reflected-light effects from the orientation of
Light
source
a
b
c
d
surface with respect to the light source in
a light microscope. (Reproduced with kind
permission of Springer Science and Business Media from Ref. [1]. © 1992 Springer
Science.)
137
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4.2 Contrast Formation
4 Scanning Electron Microscopy
in the image will appear dark. The contrast created by the trajectory effect is very
much similar to the contrast we see with our eyes of a rough surface illuminated by
oblique light. Thus, there is little problem for us to interpret topographic contrast
such as shown in Figure 4.12.
Nevertheless, topographic contrast in an SEM is not exactly the same as the
contrast achieved by inclined light illumination. In an SEM image, the electron
number effect will create bright areas in the image that do not correspond to
surface contours on the specimen. Figure 4.13 illustrates the electron number effect.
When the electron probe hits near an edge or a inclined surface, more electrons can
escape from the specimen than when the probe hits a flat surface directly. Thus,
certain areas of the specimen (such as edges of spherical particles, raised areas,
20 μm
Figure 4.12 Secondary electron image of a fracture surface along grain boundaries. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 1992
Springer Science.)
More
electrons
escape
Electron
probe
Electron
probe
Electron
probe
Fewer
electrons
escape
Figure 4.13 Electron-number effects due to surface topography. More secondary electrons
can escape from the edges of topographical features than from a flat surface.
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138
HKUST
SEI
5.0 kV X1,000 10 μm WD 7.6 mm
Figure 4.14 Secondary electron image of a cracked silicon surface. Electron-number effects
make the edges of surface cracks brighter than the rest of the surface.
and cavities) will appear bright in an SEM image. Figure 4.14 shows the example of
topographic contrast from the electron number effect. The SEM image of a silicon
specimen exhibits brighter edges of cracks than its flat surface areas, because of
the electron number effects.
Commonly, a topographic image is obtained by operating an SEM in the SE
mode. However, both SEs and BSEs contribute to topographic contrast, but SEs
are the primary signals for topographic contrast formation. Only those BSEs with
trajectories on a direct path toward the scintillator of an E–T detector contribute
to topographic contrast formation. It is important to note that in a topographic
image the surface areas that do not face the detector are not totally dark. The SEs
from such surface areas can be drawn to the detector when the Faraday cage is
positively charged, as shown in Figure 4.3, because SEs with low kinetic energy
readily change their trajectories.
4.2.3
Compositional Contrast
Compositional contrast refers to the variation in gray levels in an SEM image that
correspond to variation in chemical composition in a specimen. An image formed
by BSEs exhibits very useful compositional contrast if the specimen consists of
more than one chemical element. The origin of compositional contrast arises
because the capability of BSEs to escape from the specimen depends on the atomic
numbers of the specimen atoms. The backscatter coefficient (η) characterizes such
capability
η=
nBSE
ni
(4.10)
139
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4.2 Contrast Formation
4 Scanning Electron Microscopy
η is the ratio of the number of BSEs escaping from the specimen (nBSE ) to
the number of incident electrons (ni ). It increases monotonically with the atomic
number as shown in Figure 4.15. Thus, any area in a specimen containing chemical
elements with higher atomic number will generate more BSEs. The difference in
the number of BSEs collected by a detector will appear as differences in gray levels
in a black and white image; that is, an area with atoms of higher atomic numbers
will appear brighter. Thus, a BSE image shows the atomic number contrast or
compositional contrast, as demonstrated in Figure 4.16, in which there is a sideby-side comparison of an SE image and a BSE image for the same surface area of
Backscatter coefficient, η
0.6
0.5
5 keV
0.4
10 keV
0.3
20 keV
30 keV
0.2
40 keV
0.1
0.0
49 keV
0
20
40
60
Atomic number
80
100
Figure 4.15 Backscatter coefficient as a function of atomic number of specimen atoms.
(Reproduced with kind permission of Springer Science and Business Media from Ref. [1].
© 1992 Springer Science.)
160X
200UM
25KV WD : 12MM
E T POSITIVE
(a)
160X
200UM
S : 00000 P : 00032
25KV WD : 12MM
S : 00000 P : 00033
BSE SUM
BIAS
(b)
Figure 4.16 Comparison between: (a) a secondary electron image and (b) a backscattered
electron image for the same area of a nickel alloy. Additional compositional information is
obtained from the backscattered image. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 1992 Springer Science.)
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140
a nickel alloy. The SE signal also contributes to compositional contrast, but such
contrast is small and unpredictable, mainly because the intensity of an SE signal
does not have strong dependence on the atomic number.
When the E–T detector is used for compositional contrast, the Faraday cage
should be negatively charged (−50 V) to exclude SEs with energies lower than the
bias voltage of the cage. Some SEM systems are equipped with a dedicated detector
for BSE collection, which is placed above the specimen. To obtain compositional
contrast, we can switch detection from the SE mode to the BSE mode by simply
pushing a button on the SEM control panel.
In additional to topographic and compositional contrast, there are other types of
contrast in the SEM, in particular, crystallographic contrast and magnetic contrast.
Crystallographic contrast is also called the contrast of electron channeling. It arises
because the BSE coefficient is dependent on the orientation of crystallographic
planes with respect to the direction of the electron beam. The plane orientation
affects the penetration of the electron beam into the crystal because the atomic
packing density varies with crystallographic plane. For higher penetration, the
backscattering coefficient is lower. A large single-crystal surface may exhibit an
electron channeling pattern that reveals the crystal orientation of a specimen
surface layer (∼50 nm). The electron channeling image in an SEM is very similar
to the Kikuchi pattern in a TEM. The magnetic domains of ferromagnetic materials
may also exhibit special contrast in SEM. Detailed discussion of such contrast can
be found in the references listed at the end of Chapter 4.
4.3
Operational Variables
It is necessary to understand the operational variables to obtain a good SEM image
with desired depth of field and resolution. This section discusses how to control the
depth of field and resolution by adjusting operation variables such as the working
distance, final aperture size, acceleration voltage, probe current, and astigmatism.
4.3.1
Working Distance and Aperture Size
The working distance and aperture size, illustrated in Figure 4.4, are the operational
variables that strongly affect depth of field. We often need to make full use
of the most important feature of an SEM: the three-dimensional appearance of
topographic images. Recall that the depth of field is related to the resolution (R)
and the convergence angle of objective aperture (α) as Eq. (1.7).
2R
tan α
The resolution of an SEM image on a display screen is limited by the pixel size of
the screen. The product of the resolution and the SEM magnification (M) should
be equal to the pixel size. Suppose that the pixel size is 100 μm, the resolution
of a SEM image on the display screen can be expressed as 100 M− 1 μm. The
Df =
141
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4.3 Operational Variables
4 Scanning Electron Microscopy
Table 4.1
Depth of field of an SEM image (μm).
α f (rad)
Magnification
5 × 10− 3
1 × 10− 2
3 × 10− 2
4000
800
400
80
40
4
0.4
2000
400
200
40
20
2
0.2
670
133
67
13
6.7
0.67
0.067
10×
50×
100×
500×
1 000×
10 000×
100 000×
Data taken from Ref. [1]. © 1992 Springer Science.
convergence angle of an SEM probe (α f ) is much less than 1 rad. Thus, the depth
of field in SEM can be expressed as follows.
200
(μm)
(4.11)
Df ∼
=
αf M
Table 4.1 lists the depth of field as a function of the convergence angle and
magnification. α f is controlled by the final aperture radius and the working
distance between the aperture and specimen surface (Figure 4.4). Equation (4.11)
can be rewritten to express the depth of field as a function of the aperture radius
(Rfap ) and the working distance (DW ) as follows.
200 DW
(μm)
Df ∼
=
Rfap M
(4.12)
Equation (4.12) simply tells us how to control the depth of field in an SEM
by changing the aperture size and working distance. Figure 4.17 illustrates the
relationships among depth of field, aperture size, and working distance. A small
aperture size and a long working distance results in a high depth of field. The SEM
micrographs in Figure 4.18 show the differences in the depth of field when the
aperture radius changes from 25 to 85 μm and the working distance changes from
25 to 48 mm. The aperture size and working distance can be easily changed during
SEM operation.
Although selecting a combination of small aperture size and long working
distance is favorable for high depth of field, such operation will result in negative
effects on image resolution. A small aperture size reduces the probe current,
and also may reduce the ratio of signal-to-noise. A long working distance is not
desirable because it will decrease α f if the aperture size is unchanged. A small
α f is not favorable for high resolution. Further, a long working distance increases
the spherical aberration of a lens and consequently worsens the SEM resolution.
Considering such tradeoffs between resolution and depth of field, it is wise to select
an intermediate aperture size and intermediate working distance, unless a very
large depth of field or very high resolution is required.
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142
Aperture diameter
Electron beam
Working
distance
Depth
of field
Sample
Figure 4.17 Relationship between the depth of field, aperture size, and the working
distance.
20KV
100 μm
X300
(a)
100 μm
X300
20KV
100 μm
X300
(b)
20KV
(c)
20KV
100 μm
X300
(d)
Figure 4.18 Effects of final aperture radius (Rfap ) and working distance (DW ) on the depth
of field: (a) 25-mm DW , 85-μm Rfap ; (b) 25-mm DW , 25-μm Rfap ; (c) 48-mm DW , 85-μm
Rfap ; and (d) 48-mm DW , 25-μm Rfap .
143
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4.3 Operational Variables
4 Scanning Electron Microscopy
4.3.2
Acceleration Voltage and Probe Current
As discussed in Section 4.1.3, the probe size and probe current are critical to
achieving high-resolution SEM images. The acceleration voltage of the electron
gun, and probe current, are two primary operational variables used to adjust the
resolution. Recall that acceleration voltage is the controlling factor of probe size,
because the probe diameter decreases with decreasing wavelength of electrons, and
the wavelength is, in turn, determined by acceleration voltage. Thus, increasing the
acceleration voltage, which is equivalent to decreasing the wavelength, will reduce
the probe size. The benefit of voltage increase is reflected in increases in electron
beam brightness (Eq. (4.2)), which also results in reduction of the probe size.
Figure 4.19 shows a comparison of the resolution of SEM images when selecting
5 and 20 kV, while maintaining other operational variables constant. The image at
20 kV reveals more surface details on a specimen of etched titanium than that at
5 kV because of higher resolution.
On the other hand, the negative effects of selecting higher voltage, which are
due to the interaction between electron probe and specimen materials, should
not be ignored. A higher voltage causes an increase in the interaction zone in
the specimen, as illustrated in Figure 4.10. An increase in the interaction zone
in lateral directions will result in a decrease in the lateral spatial resolution of
SEM images. Currently, more and more SEM systems are being equipped with
field emission guns, which provide high electron beam brightness without a high
acceleration voltage. In a field-emission SEM system, a relatively low acceleration
voltage (∼5 kV) can also achieve high electron beam brightness and a small probe
size.
Adjustment of the probe current during operation will help us to balance the
requirements of probe-size reduction by lowering probe current, and of signal-tonoise ratio. A low probe current produces weak signals collected by the detector.
20kV
(a)
X5,000
5 μm
10 40 SEI
5kV
X5,000
5 μm
10 40 SEI
(b)
Figure 4.19 Comparison of the effect of acceleration voltage on topographic contrast of
acid-etched titanium specimen. (a) 20 kV and (b) 5 kV.
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144
15KV
1 μm
X20,000
(a)
15 mm
15KV
1 μm
X20,000
15 mm
(b)
Figure 4.20 Effects of astigmatism: (a) blurred astigmatic image and (b) sharp image after
astigmatism has been corrected.
An excessive gain on the signal amplifier is needed for image formation when the
probe current is too low. The excessive gain will generate a high level of electronic
noise in an SEM image. Adjustment of probe current is necessary whenever the
acceleration voltage and magnification are changed during operation. However, the
importance of adjusting probe current is often neglected during SEM operation.
4.3.3
Astigmatism
Astigmatism is an operational variable that is often adjusted to obtain a good
electron microscope image. Astigmatism is the lens aberration resulting from
power differences of a lens in its lens plane perpendicular to the optical path
(Figure 1.9), which is discussed in Chapter 1. For most SEM systems, astigmatism is not a serious problem when magnification of the image is less than
10,000×. At high magnification, astigmatism effects on an image are seen, as
demonstrated by Figure 4.20. An image with astigmatism looks out of focus.
In Figure 4.20a, the images of small particles are stretched by astigmatism. This
can be conveniently corrected using the stigmator knobs on the SEM control
panel. The stigmator adjusts the electromagnetic field of the objective lens in two
perpendicular directions in order to eliminate the asymmetrical distortion of the
lens. Figure 4.20b shows the same image as Figure 4.20a after correction by the
stigmator.
4.4
Specimen Preparation
A specimen for SEM analysis can be in any form; such as bulk, power, thin film,
and so on. This is one of reasons that SEMs are more widely used than TEMs,
145
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4.4 Specimen Preparation
4 Scanning Electron Microscopy
which requires a foil type of specimen. However, there are special problems in
SEM specimen preparation such as surface charging of specimens that have poor
electric conductivity, and dehydration requirement for biological samples.
4.4.1
Preparation for Topographic Examination
For topographic examination, we should do minimal preparation of specimens
in order to preserve features of their surfaces. The preparation should involve
only sizing the specimens to fit a SEM specimen holder and removing surface
contaminants. The specimen holder of an SEM varies with manufacturer. Some
SEM systems can hold a specimen with dimensions of tens of centimeters.
Common contaminants on the specimen surfaces are hydrocarbons from oil
and grease, because an electron beam decomposes any hydrocarbon and leaves
a deposit of carbon on the surface. The deposit generates an artifact of a dark
rectangular mark in SEM images. Figure 4.21 shows an example of hydrocarbon
contamination on an SEM image. A dark mark is readily seen on a hydrocarboncontaining specimen at lower magnification after examining the same location at
higher magnification. The carbon deposition is formed quickly under a higher
magnification because of the higher exposure rate of electron beam.
Surfaces with oil or grease contamination should be cleaned by an organic
solvent such as methanol or acetone in an ultrasonic cleaner. It is also important to
avoid touching the cleaned specimen with bare hands because fingerprints contain
volatile hydrocarbon compounds. Sometimes a dark mark occurs on a well-cleaned
x50000
500 nm
1.00kV
3 mm
Figure 4.21 SEM micrograph of Al on TiN. The beam was first focused on the central region for about 30 s, and then the magnification was reduced. Contamination built up in the
central region is visible at reduced magnification. (Reproduced with permission from Ref.
[2]. © 1999 John Wiley & Sons Ltd.)
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146
specimen. This might result from hydrocarbon contamination from a dirty vacuum
system. Hydrocarbons escaping from the diffusion pump oil into the SEM chamber
can also contaminate a specimen under electron beam.
4.4.1.1 Charging and Its Prevention
Surface charging causes SEM image distortions and should be carefully prevented.
Surface charging is most likely encountered when examining electrically nonconductive surfaces. It occurs when there are excessive electrons accumulated on
the specimen surface where it is impinged by the electron beam. Accumulation
of electrons on the surface builds up charged regions. In such regions, electric
charges generate distortion and artifacts in SEM images. Figure 4.22 shows several
examples of SEM image distortion due to surface charging.
200 μm
(a)
(b)
(c)
15Kv
00039 100 μm
Figure 4.22 Image artifacts due to surface charging: (a) gross charging effects
on TeflonT M ; (b) negative charging of
nonconductive particles on an Al substrate, which induces positive charge
on the substrate as shown by dark contrast; and (c) charging causes unstable
signals as shown in discontinuities
when scanning a calcite crystal.
(Reproduced with kind permission of
Springer Science and Business Media from:
(a) and (c), Ref. [1]. © 1992 Springer Science; (b), Ref. [3]. © 1998 Springer-Verlag
GmbH.)
147
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4.4 Specimen Preparation
4 Scanning Electron Microscopy
Charging causes image distortion and artifacts because the charged regions
deflect the incident electron probe in an irregular manner during scanning;
charging alters SE emission, and charging causes the instability of signal electrons.
The third phenomenon can be understood as the sudden release of charge along
a conducting path when charge has accumulated to a critical level in a particular
region.
Surface charging should be a primary concern for nonconductive specimens such
as ceramics, polymers, and specimens containing biological substances. Surface
charging is generally not a problem for metallic specimens because their good
electrical conduction ensures removal of excess electrons, which cause surface
charging, to ground by electrical conduction between the specimen surface and
ground. However, a metal oxide layer and nonconductive phases in metallic
specimens may also generate surface charging.
The most common way to prevent charging is to coat a conductive film onto
specimen surfaces to be examined. Conductive coating is ordinarily accomplished
by means of either vacuum evaporating or sputtering. Vacuum evaporating deposits
conductive atoms on a specimen in a vacuum chamber. The conductive substance
has to be heated to a high temperature for it to evaporate. Sputtering strikes a
conductive target with high-energy ions that impart momentum to atoms of the
target, enabling them to leave the target and deposit on the specimen. Sputtering
is a more widely used method than vacuum evaporating for conductive coating of
SEM specimens.
Figure 4.23 shows a schematic illustration of sputtering mechanism. Argon
gas is commonly used to produce ionized gas (plasma) in sputtering. Gold is
often used as the target material. Sputter coating is more popular because of its
Ring-shaped
magnet
Gold cathode
+
+
+
+
e−
e−
e−
e−
e−
Magnetic lines
of force
e−
Stub with
sample
Anode
To vacuum pump
+
Positive argon ions
Gold particle
e−
Electron
Figure 4.23
Sputtering gold onto a specimen surface.
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148
short preparation time and coating uniformity on rough specimens. The coating
thickness is normally controlled at about 5–20 nm depending on the magnification
to be used in SEM examination. High-magnification imaging requires a thin
coating, 5 nm or less. Generally, we choose a thinner coating as long as it ensures
conduction and surface coverage. A thick layer tends to be granular and cracked,
which may distort the original topographic features of specimen surfaces.
A potential problem associated with sputtering is the possibility of thermal
damage to sensitive specimens. Heating of the specimen during coating can cause
cracking, pitting, and melting, particularly for organic specimens. To avoid these
problems, cool sputtering, known as plasma–magnetron sputtering, can be used.
Plasma–magnetron sputtering can maintain the specimen at ambient temperatures by introducing a magnetic field to manipulate the plasma flow and reduce
heating of the specimen.
4.4.2
Preparation for Microcomposition Examination
Any specimen prepared for topographic examination is generally suitable for
composition examination using the BSE mode. Electrical conduction of specimen
surfaces is still required for compositional examination. A specimen prepared
for light-microscopy examination may also be directly used for composition examination in an SEM. If the specimen is either not metallic or is a metallic
specimen mounted in a nonconductive substrate, we should coat the specimen
for composition examination as for topographic examination. It is common that
an SEM specimen for composition examination is mounted in conductive epoxy
resins or conductive thermoplastics before it is ground and polished, similar to
the preparation of a LM specimen. The etching used for light microscopy is not
necessary for compositional contrast using the BSE mode, while deeper etching is
required for topographic contrast using the SE mode.
For polymer specimens, we can use a heavy-metal element to stain the specimens to generate compositional contrast, similar to preparing polymer specimens
for TEM. Compositional contrast resulting from staining can reveal a polymer
specimen containing multiple phases because the staining level of the heavy-metal
element varies with molecular structures of polymer phases. Table 4.2 lists the
staining agents for various polymer functional groups.
4.4.3
Dehydration
Dehydration is a special preparation technique required to examine a specimen
containing water in an SEM. Any specimen derived from or containing biological
substances may need processing to remove water. If water is not removed, the
high-energy electron beam will heat the water in the specimen and cause it to
burst through the specimen surface, thus destroying the surface morphology of
the specimen. Dehydration may be accomplished either by critical-point drying or
149
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4.4 Specimen Preparation
4 Scanning Electron Microscopy
Table 4.2
Polymer functional groups and staining agents.
Polymer groups
Staining agents
Unsaturated hydrocarbons, alcohols, ethers, amine acids,
esters
Unsaturated rubber
Saturated hydrocarbons:
polyethylene (PE) and polypropylene (PP)
Amides, esters, PP
Ethers, alcohols, aromatics, amines, rubber, bisphenol A,
styrene
Esters, aromatic polyamides
Acids, esters
Osmium tetroxide
Ebonite
Chlorosulfonic acid/uranyl acetate
Phosphotungstic acid
Ruthenium tetroxide
Silver sulfide
Uranyl acetate
freeze-drying. These techniques remove water from a specimen without collapsing,
flattening, or shrinking the specimen. Figure 4.24 shows an example of using
specimen dehydration before examining the behavior of bone cells on microgrooves
of calcium phosphate substrate. The cell morphology, which is critical for evaluating
interactions between bone cells and the substrate, is preserved by critical-point
drying.
The critical point refers to the certain combination of temperature and pressure
at which the liquid density is equal to the vapor density. At its critical point, liquid
will become vapor and is easily removed. We cannot directly remove water using its
critical point because the temperature and pressure of the critical point (374 ◦ C and
HKUST
10KV
10 μm
X500
14 mm
Figure 4.24 SEM micrographs of osteoblasts (a type of bone cell) on the microgrooved
surface of calcium phosphate.
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150
22 MPa) are too high and may damage the specimen. Alternatively, we can replace
water with a transitional fluid that has a critical point with lower temperature and
pressure. Liquid CO2 or Freon is often used as the transitional fluid. The critical
point for liquid CO2 is 31.1 ◦ C and 7.4 MPa. The common procedure is described as
follows. First, the water content in a specimen is removed by dehydration with an
ethanol series (30, 50, 75, and 100%). Then, the dehydrated specimen is transferred
into an ethanol-filled and cooled chamber in the critical-point drying apparatus. The
transitional fluid is introduced until it completely displaces ethanol in the chamber.
The chamber is gradually heated and pressurized to reach the critical point of the
transitional fluid. After reaching the critical point, the transitional fluid vaporizes,
and this vapor is slowly released from the chamber until atmospheric pressure is
reached. Then, we can retrieve the intact, dry specimen from the chamber.
The freeze-drying method uses sublimation (solid to vapor transformation) to
dry specimens. This method requires freezing a specimen rapidly to below −80 ◦ C
in a chamber. At that temperature, the chamber is degassed under a low pressure
of less than 0.1 Pa. The specimen can be dried in such a condition after several
hours to several days.
4.5
Electron Backscatter Diffraction
Electron backscatter diffraction (EBSD) is a technique to determine crystalline
materials properties in electron microscopy (both SEM and TEM, but mainly
used in the SEM system). With special detector, an SEM system can record EBSD
patterns of a crystalline solid, which are essentially the backscatter Kikushi patterns.
With the EBSD patterns, we can determine crystalline orientations of individual
grains of a polycrystalline specimen and identify separate crystalline phases in a
multiphase specimen. The EBSD technique is increasingly used for examining
metallic and ceramic materials, particularly for metals.
4.5.1
EBSD Pattern Formation
Figure 4.25 illustrates the formation principles of EBSD patterns, the backscatter
Kikushi patterns. As Kikushi line formation in TEM, EBSD requires incident
electrons inelastically scatter in a specimen. When the primary electron beam
of SEM focused on a location of a specimen, S (tens of nanometers from the
specimen surface), the electrons scatter from S to all directions in a crystalline
solid. There must be an electron beam with the scattering angle (θ ) from the scatter
location to a certain crystallographic plane that satisfies the constructive diffraction
condition, Bragg’s law (Eq. (2.3)). The constructively diffracted electron beams can
be recorded by a detector a short distance away from the specimen surface, as
illustrated in Figure 4.25a. In fact, the diffraction beams with the same θ angle
form two symmetric cone surfaces with respect to the scatter source location S ,
151
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4.5 Electron Backscatter Diffraction
4 Scanning Electron Microscopy
Incident
electron beam
e−
Diffraction
cones
θ
θ
2θ
S
Interaction zone
dhkl
Screen
Screen
(a)
Specimen
70°
(b)
Figure 4.25 (a, b) Schematic illustration of EBSD formation principles. Scattering of electrons from S near the surface of the specimen generates a Kikushi band of crystallographic
plane with spacing dhkl .
because of the three-dimensional nature of specimen. The intersections between
the cone surfaces and a detector screen generate two parallel lines (Kikushi band)
as the EBSD of a specific crystallographic plane, for example, (110). Thus, we can
understand that each band in ESBD patterns represents a crystallographic plane
(hkl). By indexing all the bands in an EBSD pattern, we are able to determine the
structure of a crystal and its orientation respect to the plane of detection screen.
Figure 4.26 illustrates the EBSD instrumentation arrangement in SEM. The
specimen surface must have a large title angle (∼70◦ ) with respect to the primary
electron beam. The detector is mounted with this phosphor screen facing the
specimen with a short detection distance (∼20 mm). The phosphor screen is
commonly parallel to the primary electron beam, with a tilt capability of about 20◦ .
Incident
beam
CCD
camera
Phospher
screen
Backscatter
electrons
Figure 4.26 Schematic illustration of instrumental arrangement of incident electron beam,
specimen, phosphor screen, and recording CCD camera for EBSD patterns in SEM.
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152
153
In addition to the phosphor screen, the EBSD detector includes a CCD (chargedcoupled device) camera at the back of the transparent phosphor screen that records
the EBSD patterns digitally. To obtain EBSD patterns, an SEM is commonly
operated with acceleration voltage of 10–30 kV. High beam current is required for
EBSD (0.5–10 nA) and the corresponding electron probe diameter is in the range
of 0.02–0.5 μm. We should know that the EBSD signals exhibit low signal/noise
ratios. Thus, detection of EBSD patterns requires a highly sensitive CCD camera
and integrating of multiple frames of the same EBSD patterns. The EBSD sampling
mode can be either stage-scan or beam-scan. The stage-scan mode keeps the primary
electron beam stationary and mechanically moves the specimen stage with respect
to the beam. The beam-scan mode keeps the specimen stationary and moves the
primary beam across the specimen surface.
The specimens for EBSD can be any type of crystalline material that is stable
under a high-intensity electron beam; including most metals, ceramics, and
semiconductors. Specimen surfaces should be flat with a surface polish similar to
that for metallographic specimens for light microscopy. Also, the surface with tens
of nanometer thickness should be free from residual stress and strain that may be
generated during its preparation process.
4.5.2
EBSD Indexing and Its Automation
Figure 4.27 shows a typical EBSD pattern that you may find similar to the
Kikushi pattern (Figure 3.38) obtained in TEM. Each Kikushi band represents a
crystallographic plane (hkl). The band width is proportional to the planar spacing,
dhkl , of plane (hkl). The angle between two bands is directly related to their
interplanar angle. Moreover, the bands of the crystal planes belonging to a crystal
zone intersect each other in the pattern. The zone axis locates at the intersection
-1-2-1
0-10
1-21
-1-30
0-31
-1-20
0-21
-1-10
-1-21
0-11
-2-10
-1-11
-2-11
(a)
(b)
Figure 4.27 (a) An EBSD pattern of pure copper acquired in SEM (b) and its pattern
indexing by a computer software. (Reproduced with permission of Jingshen Wu and
Dong Liu.)
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4.5 Electron Backscatter Diffraction
4 Scanning Electron Microscopy
center of bands with the axis direction perpendicular to the pattern surface. With
knowledge of the crystal plane symmetry respect to the zone axis, we may be able to
determine the individual zone axis, such as [110] and [121] marked in Figure 4.27b.
Indexing an EBSD pattern includes identifying individual bands and individual
zone axis, which could be a tedious task. Fortunately, a modern EBSD system is
equipped with computer software that can automatically index EBSD patterns after
being recorded by a CCD camera.
We should note that a digital image of EBSD pattern recorded by a CCD camera
is composed of numerous pixels. A Kikushi band in the image is a collection of a
certain type of pixel. For example, as shown in Figure 4.27a, the Kikushi band is
whiter than its background. To identify a Kikushi band requires identifying those
white pixels (dots) that belong to a band (line). It is not difficult for a human to
perceive a line in an image, but it is rather difficult task for a computer. Noting
that to identify a point is easier than a line, a special technique is used to convert
a line to a point, named the Hough transform, for the band recognition task in a
computer.
A Hough transform is a mathematical operation that can represent a line a point and
identify a line in real space from a point in a transform space. In a conventional (x,y)
coordinate plane, we can represent a line by equation (y as linear function x). If we use
a polar coordinate with parameters ρ (the distance from origin to line) and θ (the angle
between ρ 1 and x direction), the line equation should be (Figure 4.28a)
ρ = x cos θ + y sin θ
(4.13)
However, in the (ρ, θ ) space, the equation is represent by a single point (ρ, θ ). This
means that a line in (x,y) space become a point in (ρ, θ ) space. On the other hand, a
single point in a (x,y) space will be presented by a sinusoidal line (with fixed x and y
value) according to Eq. (4.11) (Figure 4.28b). Thus, a number of points belonging to
one line in (x,y) space will be presented as a number of lines in (ρ, θ ) space passing
through a single point. By transforming pixels in an EBSD image to lines and finding
the intersection point of those, the Kikushi band can be recognized by a computer. With
12
10
6
ρ
Y
8
4
2
0
(a)
0
1
2
3
X
4
5
6
9
8
7
6
5
4
3
2
1
0
0
(b)
xy(1,8)
xy(3,4)
xy(2,6)
xy(4,2)
10 20 30 30 50 60 70 80 90 100
θ
Figure 4.28 (a, b) Illustration of a Hough transformation. A line in the (x,y) space become
a point in the (θ ,ρ) space. The points in a line of (x,y) space become lines in the (θ ,ρ)
space with a single intersection point which represents the line.
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154
a database of crystallography, a computer can index all the crystallography planes and
zone axes in ESBD patterns, as shown in Figure 4.27b, without human interference.
4.5.3
Applications of EBSD
The most widely used applications of EBSD are determination of grain orientations
and identification of phase phases in crystalline materials. By stepwise scanning
through a specimen surface, the EBSD patterns of individual microscopic areas will
be collected and indexed automatically. Differences of crystal orientation among
grains can be revealed by the differences in EBSD patterns. This method is especially
useful for analyzing texture structures of metals resulting from processing such
as solidification, plastic deformation, and heat treatment. Figure 4.29 shows an
example of an EBSD application in determining grain orientations of a magnesium
alloy. The computer software can graphically represent the orientation differences
among grain with colors or gray levels. Commonly higher contrast between
grains means a greater difference in grain angle. Grain boundaries are effectively
identified by small-step acquisition of EBSD patterns. With a large number of
grain-orientation data, a texture structure can be quantitatively analyzed by EBSD
techniques.
EBSD phase identifying a microscopic area of a specimen is more complicated
than determining its grain orientation of a known phase. However, the phaseidentification principle is the same as that of X-ray diffractometry and electron
diffraction in TEM; that is, a crystalline phase can be identified by determining the
interplanar spaces of crystallographic planes. EBSD identifies interplanar spaces by
-200 μm
Figure 4.29 EBSD reveals the grain-orientation differences in an annealed magnesium
alloy. The gray levels represent the levels of orientation-angle differences among grains.
(Reproduced with permission of Renlong Xin).
155
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4.5 Electron Backscatter Diffraction
4 Scanning Electron Microscopy
measuring band widths and determining interplanar angles from angles between
bands, and then searching for a match in crystallographic database. Moreover,
the EBSD pattern provides symmetry information of zone axes that helps in
determining the crystal system of the phase to be identified. Commonly, we should
reduce the phase search of a microscopic area based on its chemical information
that can be obtained by microanalysis using X-ray EDS in SEM. With composition
information provided by EDS, the phase search can be limited to several possible
phases in that microscopic area. With limited possible phases, computer software
can quickly find the best phase matching in crystallographic databases.
4.6
Environmental SEM
An environmental scanning electron microscope (ESEM) is a special type of SEM
system that allows specimens to be examined under gaseous environments, which
is extremely useful to examine hydrated specimens and biological specimens containing water naturally. ESEM may have other names, such as variable-pressure
scanning electron microscope (VP-SEM), wet-SEM, and so on, given by its manufacturing company. As mentioned in this chapter, a conventional SEM system
requires that specimens must be examined in a high-vacuum chamber for two
main reasons: (i) an electron gun can only be operated in high vacuum conditions
and (ii) an electron beam can only be focused on a specimen without severe scattering by gaseous molecules. To overcome these barriers of examining specimens
in nonvacuum environments, ESEM has a special design to separate the specimen
chamber in a gaseous environment with the main high-vacuum chamber in an
SEM system. We should note that commercial ESEM is actually a low-vacuum
SEM because the gaseous pressure of the specimen chamber is limited up to
thousands of pascals (tens of torr), which is much lower that the atmosphere
pressure of 101 000 Pa (760 torr). A low gaseous pressure environment, however,
is sufficient for us to observe a specimen in the hydrated state. Also, ESEM adopts
a short working distance to limit the scattering of the primary electron beam in the
specimen chamber.
4.6.1
ESEM Working Principle
The key of ESEM design is to divide the SEM column into two chambers with the
pressure-limiting aperture (PLA) as illustrated in Figure 4.30. PLA can maintain the
main part of SEM column in a high-vacuum condition, including the electron gun
and the main pathway of the electron beam to objective lens; while allow a certain
level of gas pressure to be built up in the specimen chamber. PLA has a small orifice
that effectively prevents leakage of gas from the specimen chamber, while allowing
the primary electron beam to pass through. The common design of ESEM has two
or more PLAs so that gas leaked through the first PLA can be quickly removed from
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156
Gun
Ultrahigh vacuum
Pump
PLA2
Gas
High vacuum
Pump
PLA1
Specimen
low vacuum
Pump
Figure 4.30 Schematic illustration of environmental SEM instrumentation. The specimen
chamber is separated with an ultrahigh vacuum chamber by two pressure-limiting apertures
(PLA1 and PLA2).
the column by the first-stage differential pumping and further gas leaking through
the second PLA will be pumped out by the second-stage differential pumping.
ESEM has to ensure that the electron beam can reach a specimen without
severe scattering by gaseous molecules. This is possible under an oligo-scattering
condition in which a focused beam on a specimen surface is surrounded by a
‘‘skirt’’ of scattering electrons, as illustrated in Figure 4.31. In such a case, the skirt
of electrons will generate background noise on an SEM image, but not affect the
resolution, which is determined by the focused beam itself.
To achieve the oligo-scattering condition, acceleration voltage, gas pressure, and
distance between the first PLA to specimen have to be carefully selected. For a
given acceleration voltage and gas, the higher the gaseous pressure, the lower the
Skirt electrons
(a)
(b)
Figure 4.31 Schematic illustration of oligo-scattering condition of ESEM electron beam in
(b), comparing it with the condition of a conventional SEM in (a).
157
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4.6 Environmental SEM
4 Scanning Electron Microscopy
Primary beam
Annular anode
Annular anode
E
Gas molecule
Cathode
Specimen
Figure 4.32 Schematic illustration of gaseous detection device (GDD) that is located above
a specimen with annular shape, and avalanche effect of signal electron collisions with gas
molecules.
distance should be. The product of pressure (P) and working distance (L) should
be a constant, PL = Constant (Pa m), for a certain acceleration voltage. From this
relation, we might appreciate the difficulties encountered when gaseous pressure
increases in the specimen chamber by realizing the limit of reducing the distance
between the PLA and the specimen. Commonly, the working distance is limited to
10 mm or less.
The signal electron detection system in ESEM is also different from a conventional SEM. The E–T detector in conventional SEM does not work in a gaseous
environment because the high bias voltage associated with the detector will generate
electrical discharge (arcing) in a gaseous environment. A special gaseous detection
device (GDD) is used for signal electron detection in ESEM. Its work principle is
quite simple, as shown in Figure 4.32. A positively biased annular electrode (served
as anode) is placed above the specimen (serving as a cathode). Signal electrons are
driven toward the annular electrode by the electric field between the specimen and
the anode. On the way to the anode, the signal electrons are multiplied because
the electrons collide with gaseous molecules and release new electrons on the way
to the anode (an avalanche effect). The GDD system can reach 100% efficiency,
which is better than the E–T detector; with properly designed annular anode size,
distance between anode and specimen and electrical field strength. GDD can detect
both the signals of SEs and BSEs. Those two electron signals can be separated
because SEs dominate in the inner gaseous volume around primary electron beam
and BSEs dominate in the outer gaseous volume between a specimen and GDD.
4.6.2
Applications
ESEM exhibits great advantages in examining hydrated specimens containing
water. A hydrated specimen can maintain its water phase for a temperature higher
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158
Figure 4.33 ESEM image of hydrated clotted erythrocytes (red blood cells), Temperature
T = 6 ◦ C, water pressure P ∼470 Pa (3.5 torr). (Reproduced with permission from Ref. [4]
2008 John Wiley & Sons Ltd.)
than 0 ◦ C as long as the gaseous pressure is over several hundred pascals. Thus,
the dehydration process is not necessary for hydrated specimens being examined
in SEM and possible morphology distortion associated with dehydration can be
avoided. Figure 4.33 shows the ESEM image of hydrated clotted red blood cells
with water pressure of 470 Pa.
ESEM also allow electrically insulated materials to be examined without conductive coating. This feature results from neutralization of surface charging by
ionized-gas molecules. As mentioned in this chapter, surface charging is a serious problem for a specimen with poor electrical conductivity. Primary electron
accumulations on specimen severely distort SEM imaging. However, in ESEM,
positively charged ions that are generated by primary electrons collisions with
gaseous molecules, can eliminate the negative charging of primary electrons to a
great extent. Thus, a conductive surface coating such as gold and carbon coating
may not be necessary for an insulator specimen.
In addition, ESEM can exhibit an antcontamination ability of imaging specimens.
In conventional SEM, a specimen may be contaminated by oil vapor of the vacuum
pumps, dirt on the chamber wall, and the specimen’s carbon-containing deposit.
Such contaminations result in dark marks in SEM imaging, as shown in Figure 4.21.
Such contamination is significantly reduced or eliminated in ESEM, because such
contaminants on specimen surfaces are desorbed by the combined interactions of
primary electrons with gaseous molecules and the specimen surface.
Questions
4.1
Compare light microscopy, transmission electron, and scanning electron
microscopy in terms of optical arrangement, illumination source, working
159
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4.6 Environmental SEM
4 Scanning Electron Microscopy
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
environment, imaging formation mechanism, and specimen preparation;
discuss their similarities and differences.
Does the objective lens in SEM play a similar role as in TEM?
Why does the field emission gun generate higher resolution of SEM than a
thermionic gun?
Estimate the effective magnifications of an SEM image showing on your
computer screen when the probe size varies between 1 nm and 1 μm.
Why do people often increase acceleration voltage to obtain better resolution
in SEM? Is any negative effect of increasing acceleration voltage on SEM
imaging?
To obtain the minimum contrast of 5% with 60 s for each frame scanning,
what should the probe current be? Compare SEM image resolution if the
acceleration voltage of 10 kV is used. (Hint: use Figures 4.8 and 4.5).
Given a specimen with surface fracture features with high differences up to
50 μm, how do you select SEM operation parameters to ensure the whole
field is in focus?
Why do people often reduce working distance to obtain a higher resolution?
What is a possible negative effect on imaging with a short working distance?
When we find that the noise level is too high in an SEM image, how can we
reduce noise by adjusting operational parameters?
Can backscattered electrons generate the same levels of resolution as secondary electrons? Why?
In an SEM image with composition contrast as shown in Figure 4.16b, which
areas contain the heavy metallic elements: bright or dark? Explain.
Is it possible to eliminate surface charging of a polymer sample without a
conductive coating? Explain.
References
1. Goldstein, J.I., Romig, A.D. Jr.,
Newbury, D.E., Lyman, C.E., Echlin,
P., Fiori, C., Joy, D.C., and Lifshin, E.
(1992) Scanning Electron Microscopy and
X-Ray Microanalysis, 2nd edn, Plenum
Publishing, New York.
2. Brandon, D. and Kaplan, W.D. (1999)
Microstructural Characterization of
Materials, John Wiley & Sons, Ltd,
Chichester.
3. Reimer, L. (1998) Scanning Electron Microscopy, Physics of Image Formation and
Microanalysis, 2nd edn, Springer-Verlag,
Berlin.
4. Iliescu, M., Hoemann, C.D., Shive,
M.S., Chenite, A., and Buschmann,
M.D. (2008) Ultrastructure of hybrid
chitosan-glycerol phosphate blood clots
by environmental scanning electron
microscopy. Microsc. Res. Tech., 71(3),
236–247.
Further Reading
Goldstein, J.I. and Yakowitz, H. (1977) Practical Scanning Electron Microscopy, Plenum
Publishing, New York.
Flegler, S.L., Heckman, J.W. Jr., and
Klomparens, K.L. (1993) Scanning and
Transmission Electron Microscopy, an Introduction, W.H. Freeman, New York.
Goodhew, P.J. and Humphreys, F.J. (1988)
Electron Microscopy and Analysis, 2nd edn,
Taylor & Francis, London.
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160
Bozzola, J.J. and Russell, L.D. (1998) Electron
Microscopy, 2nd edn, Jones and Bartlett
Publishers, Sudbury, MA.
Schwartz, A.J., Kumar, M., and Adams,
B.L. (2000) Electron Backscatter Diffraction in Materials Science, Kluwer Academic/Plenum Publisher, New York.
Stokes, D.J. (2008) Principle and Practice of Variable Pressure/Environmental
Scanning Electron Microscopy (VPESEM), John Wiley & Sons, Ltd,
Chichester.
161
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Further Reading
5
Scanning Probe Microscopy
Scanning probe microscopy (SPM) is a technique to examine materials with
a solid probe scanning the surfaces. The SPM is relatively new for materials
characterization compared with light and electron microscopy. It examines surface
features whose dimensions range from atomic spacing to a tenth of a millimeter.
The SPM is considered the most powerful tool for surface structure examination
currently available because it lets us ‘‘see’’ atoms. SPM started with the scanning
tunneling microscope (STM) invented in 1982. An STM uses a tunneling current, a
phenomenon of quantum mechanics, to examine material surfaces. The tunneling
current flows through an atomic-scale gap between a sharp metallic tip and
conducting surface atoms. The SPM added a popular member, the scanning force
microscope (SFM), which was invented in the late 1980s. An SFM is commonly
called an atomic force microscope (AFM). It uses near-field forces between atoms
of the probe tip apex and the surface to generate signals of surface topography. The
AFM is more widely used than the STM because it is not restricted to electrically
conducting surfaces.
5.1
Instrumentation
The main characteristic of the SPM is a sharp probe tip that scans a sample surface.
The tip must remain in very close proximity to the surface because the SPM uses
near-field interactions between the tip and a sample surface for examination. This
near-field characteristic eliminates the resolution limit associated with optical and
electron microscopy as discussed in the previous chapters, because their resolution
is limited by the far-field interactions between light or electron waves and specimens.
Diffraction of light or electron waves associated with far-field interactions limit their
resolution to wavelength scales. The near-field interactions in a SPM, however,
enable us to obtain a true image of surface atoms. Images of atoms can be obtained
by an SPM because it can accurately measure the surface-atom profiles in the
vertical and lateral directions. The lateral and vertical resolutions of an SPM can
be better than 0.1 nm, particularly the vertical resolution. The lateral range of an
SPM measurement is up to about 100 μm, and its vertical range is up to about
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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163
5 Scanning Probe Microscopy
Table 5.1
Comparison of surface microscopy techniques.
Operating
environment
Depth of field
Depth of focus
Lateral resolution
Vertical resolution
Magnification range
Sample preparation
requirements
Sample
requirements
Optical microscopy
(reflected)
SEM
SPM
Ambient, liquid,
vacuum
Small
Medium
1.0 μm
N/A
1 × −2 × 103 ×
Polishing, etching
Vacuum
Ambient, liquid,
vacuum
Medium
Small
0.1–3.0 nm
0.01 nm
5 × 102 × −108 ×
None
Not completely
transparent to light
waves
Large
Small
1–10 nm
N/A
10 × −106 ×
Dehydrated, often
conductive coating
No charge build-up
on surface
No excessive height
variations on surface
N/A = Not applicable.
Probe
motion
sensor
Scanner
10 μm. However, the SPM must operate in a vibration-free environment because
the probe is only an atomic distance away from the examined surface. Table 5.1
provides a brief comparison between the SPM and reflected optical and scanning
electron microscopes (SEMs).
An SPM system consists of several basic components: a probe and its motion
sensor, scanner, electric controller, computer, and vibration isolation system, as
schematically shown in Figure 5.1. These components are briefly introduced in the
following sections.
Electronic
interface
Computer
Sample
Vibration isolation system
Figure 5.1
The main components of a scanning probe microscope (SPM).
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164
5.1.1
Probe and Scanner
The probe is the basic SPM component that directly interacts with a sample surface
to be examined or measured. Either the probe can scan over a stationary surface,
or it can be stationary while the sample surface is moved by a scanner underneath.
The STM and AFM differ in probe material and in how the sensor works. In
an STM, the probe is commonly made from tungsten wire. The tungsten wire
conducts the tunneling current flowing between surface atoms and tip atoms. In
the AFM, the probe tip is commonly made from SiO2 or Si3 N4 and mounted onto
a cantilever spring. A probe motion sensor senses the spacing between the tip apex
and the sample and provides a correction signal to control the piezoelectric scanner
movement. In the STM, the tunneling current is used to sense the spacing between
the probe and the sample surface. In the AFM, near-field forces between tip and
sample detected by a beam-deflection system are used to sense the spacing.
The scanner controls the probe that moves over the sample in three dimensions
in a precise way. The scanning probe needs to be positioned with an accuracy of
1 pm (10− 12 m) if atomic resolution is required. To achieve this level of precision,
a scanner is made from piezoelectric materials.
Piezoelectric materials change shape in an electric field or generate an electric field due
to a shape change. The relative length of the change is proportional to applied voltage
(E).
L
= dij E
L
where dij is the piezoelectric coefficient; its typical value is about 0.3 nm mm−1 V−1 . Thus,
greater than 300 V is required to achieve 1 μm movement for a 10-mm long piezoelectric
tube.
Three-dimensional positioning of the scanner is obtained by placing three
piezoelectric tubes in an orthogonal arrangement, as shown in the illustration
of the STM structure (Figure 5.2). The positioning accuracy of the scanner is
determined by the characteristics of piezoelectric effects. These effects include
nonlinear and hysteretic effects of piezoelectricity, as well as creep of piezoelectric
materials. In order to obtain positioning accuracy, the scanner must be well
calibrated to eliminate or offset such piezoelectric effects.
5.1.2
Control and Vibration Isolation
A SPM is a computer-based instrument, unlike light and electron microscopes
that can operate without computers. The computer controls the scanner and probe
through an electronic interface. The interface supplies the voltages that control
the piezoelectric scanner, accepts the signal from the position sensing unit and
contains the feedback control system for keeping the spacing between sample and
tip constant.
165
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5.1 Instrumentation
5 Scanning Probe Microscopy
xyz-piezo-scanner
z
High-voltage
amplifier
y
x
IT
Probing tip
Feedback
Sample
Figure 5.2 The scanning tunneling microscope (STM) system. The scanner moves the tip
over the sample surface and the feedback loop keeps the tunneling current constant. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. ©
2004 Springer-Verlag GmbH).
The computer system processes the collected data; for some systems it even takes
over feedback control. It can also correct possible data drift during instrumental
instability as well as artifacts of tilt and curvature that can appear in topographic data
due to piezoelectric effects. The computer generates SPM surface images using the
collected data. The SPM images displayed by the computer usually are extensively
processed by powerful software. For example, three-dimensional birds’-eye-view
images and artificial color images are commonly used to enhance the contrast of
images.
A SPM must be isolated from any vibrations in its surroundings in order to
achieve high resolution because its performance relies on precise control of the
distance between the mechanical probe and sample surface. To maintain a constant
near-atomic spacing during operation, any vibration from the environment must be
eliminated. Common interference includes floor vibrations and acoustic vibration.
Isolation from floor vibration is achieved by mounting the SPM on springs, rubber
feet, or air-damped feet. Isolation from acoustic vibration is achieved by operating
the instrument in a solid box.
5.2
Scanning Tunneling Microscopy
5.2.1
Tunneling Current
STM relies on a tunneling current across a gap between the probe tip and a surface
atom for surface examination. An electric current may penetrate an isolation gap
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166
between two conductors if high voltage is applied, but this is not the tunneling
current. The tunneling current is a phenomenon of quantum mechanics. It results
from electrons penetrating an energy barrier larger than the electron energy. To
generate the tunneling current (It ), a bias voltage is applied across a gap between
the tip and the sample when the tip is kept near the sample. Without much
knowledge of quantum mechanics, we may quantify the tunneling current through
the following equation
It = Vb exp(−Cd)
(5.1)
V b is the bias voltage applied between the tip and the surface, C is a constant
that depends on the nature of the sample material, and d is the nearest distance
between the tip and the sample surface. For generating a tunneling current, only
a small bias voltage (typically between 1 mV and 4 V) is necessary when the gap
is on the scale of the interatomic distance. In an STM, the tunneling current (It )
is between 10 pA and 10 nA. The tunneling current varies exponentially when the
distance changes as indicated in Eq. (5.1). The tunneling current decays by an
order of magnitude when the vacuum gap is changed by 0.1 nm. This is why STMs
provide resolution better than 0.1 nm, a truly atomic resolution.
According to quantum mechanics, the tunneling current is proportional to the local
density of states (LDOS) of the sample at the Fermi level. The density of states is the
number of electronic states per unit energy range in a solid. The Fermi level is the highest
energy level occupied by electrons in a metal at absolute zero temperature. The LDOS
at the Fermi level is important with respect to many physical properties. In particular,
it determines the numbers of electrons that can participate in electron conduction. The
LDOS can be affected by surface chemistry. For example, a molecule adsorbed onto a
metal surface may reduce the LDOS. Thus, the LDOS contour is not equal to the surface
topographic contour. The surface topography is determined by the total charge density on
the surface. It is important to note that a surface profile generated by an STM may differ
from the surface topography of the sample.
As shown in Figure 5.2, the tunneling current is used as the input signal for
precisely controlling the motion of a piezoelectric scanner. The output signals of the
feedback loop, determined by the tunneling current input, control the piezoelectric
scanner in moving either up or down. A high-voltage amplifier provides the
necessary electric potential to activate the piezoelectric scanner. Commonly, an
STM is operated in a constant-current mode. The spacing between the tip and
sample surface maintains the tunneling current as constant during scanning.
5.2.2
Probe Tips and Working Environments
A probe tip to detect a tunneling current is made from a wire of tungsten or Pt–Ir
alloys. An electrochemical etching method produces a sharp tip of tungsten wire.
The surface oxide formed on the tip during etching must be removed to ensure
good electric conductivity. Other methods of producing the tip include mechanical
cutting or grinding. The size and sharpness determine the lateral resolution of an
167
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5.2 Scanning Tunneling Microscopy
5 Scanning Probe Microscopy
STM. Ideally, for atomic resolution, a smooth tip should have a radius of a single
atom. This is impossible to achieve practically, and in fact is not necessary because
only the outermost atoms on the tips dominate the measured tunneling current.
Thus, a single-atom asperity on the tip can function like a single-atom probe for
most purposes.
In principle, the STM can work in air and liquid environments. However, most
STM work has been done in ultrahigh vacuum. This is because most sample
surfaces in an air environment quickly develop an oxide layer. An ultrahigh
vacuum environment can prevent possible surface oxide formation and maintain
a conductive sample surface. Also, low temperature is preferred because it reduces
thermal drift and diffusion of atoms and helps to obtain a static surface image of
atoms. However, an elevated temperature provides an environment for observing
dynamic processes of atoms and molecules.
5.2.3
Operational Modes
There are four operational modes in the STM: constant current, constant height,
spectroscopic, and manipulation modes. The most commonly used is the constantcurrent mode. In the constant-current mode, the feedback loop controls the scanner
moving up and down to maintain a constant tunneling current. A corrugation
contour of the LDOS during scanning can be obtained in the constant-current
mode. The corrugation contour resolves the locations of surface atoms of the
sample because the LDOS is very sensitive to atom locations. Although the LDOS
contour is not identical to surface topography, an image generated in constantcurrent mode often fairly accurately depicts the true topography when scanning is
on a scale of a few nanometers.
The constant-height mode can provide much higher scanning rates than that of
constant current. It is useful for observing dynamic processes in which timing is
important. The constant-height mode can be obtained by turning off the feedbackloop control. This mode requires that the sample surface is well leveled without tilt.
There is also a risk of crashing the tip onto the sample surface during scanning.
The spectroscopic mode refers to the operation of recording the tunneling current
as a function of either tip–sample spacing or bias voltage. The spectroscopic mode
is useful for studying surface properties such as superconduction and molecular
adsorption on metal. To record an STM spectrograph, the tip is stopped at a position
above the sample, and the tunneling current is recorded while changing either the
spacing or bias voltage between the tip and sample.
The manipulation mode refers to operations of relocating or removing atoms
on a surface. Figure 5.3 illustrates relocating an adatom (an atom attached to the
surface) by vertical and lateral manipulation. In vertical manipulation, an adatom
is transferred from the surface to the probe tip, and then is deposited at another
location. The attachment and detachment of the atom to and from the tip is
controlled by voltage pulses. In lateral manipulation, an adatom remains adsorbed
on the surface and is moved laterally by the tip when there is a weak bond between
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168
(a)
(b)
Figure 5.3 Manipulation mode in the
STM: (a) vertical manipulation, where an
adatom forms a strong bond with the
tip and is detached from the surface,
then it is transported by the tip and redeposited on the surface and (b) lateral
manipulation where the tip forms a weak
bond with an adatom and moves it along
the line of manipulation. (Reproduced
with kind permission of Springer Science
and Business Media from Ref. [1]. © 2004
Springer-Verlag GmbH.)
the adatom and the tip. This technique has been used for serious as well as fanciful
work. For example, a scientist at the IBM Corporation made an ‘‘IBM’’ symbol with
a few atoms using the manipulation mode in an STM.
5.2.4
Typical Applications
The most exciting function of an STM is its ability to image atoms. The first
atomically resolved STM image was of a silicon surface in 1982. A Si (111) surface
was obtained by thermally annealing a silicon single crystal above 1000 ◦ C under
ultrahigh vacuum. The thermal treatment produced a sublimated surface SiO2
layer. After slowly cooling, the surface atoms were reconstructed as a special lattice
pattern. Figure 5.4 shows the reconstructed Si (111) image of a 32 nm × 32 nm
area, in which there are three surface steps separating reconstructed terraces. The
STM has been successfully used to produce atomic images of various materials
including metals (such as gold, copper, platinum, and nickel) and layered crystals
(such as graphite and MoS2 ). The STM can even image adsorbed atoms and single
molecules on surfaces.
While an STM image represents the topography of a surface, it must be interpreted carefully. The image may be altered by the bias voltage applied to a sample
because the image reflects the surface of equal LDOS. For example, in an STM study
of oxygen adsorption on an n-type GaAs (111) surface, an adsorbed oxygen atom
may appear either as a protrusion or as a depression, depending on bias-voltage directions (Figure 5.5). Correctly interpreting STM images requires an understanding
of surface chemistry and physics, as well as the mechanism of the STM.
169
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5.2 Scanning Tunneling Microscopy
5 Scanning Probe Microscopy
Figure 5.4 An STM image of a 32 nm × 36 nm area on the Si (111) planes. Surface atoms
have been reconstructed, showing 7 × 7 symmetry. Three atomic steps separate terraces.
(Reproduced with permission from Ref. [2]. © 1994 Cambridge University Press.)
(a)
(b)
Figure 5.5 Oxygen adsorbed onto a GaAs surface: (a) the sample is under negative bias
voltage (−2.6 V with respect to the tip) and (b) the sample is under positive bias voltage
(+1.5 V with respect to the tip). (Reproduced with permission from Ref. [2]. © 1994 Cambridge University Press.)
In general, the STM’s ability to obtain atom images is clearly outstanding.
Unfortunately, there are some limitations, particularly the requirements that both
the tip and sample surface are good conductors. This severely limits the materials
that can be studied and has led to the development of SFM (AFM), which is
described in Section 5.3.
5.3
Atomic Force Microscopy
5.3.1
Near-Field Forces
Like the STM, the AFM uses a very sharp tip to probe and map sample topography.
The AFM detects near-field forces between the tip and sample, instead of detecting
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170
the tunneling current. Knowledge of the near-field forces acting between tip and
sample is necessary for us to understand the AFM working principles. There are
several types of near-field forces that are briefly described as follows.
5.3.1.1 Short-Range Forces
The short-range forces refer to atomic forces between atoms when their distance is
close to atomic spacing. Overlapping of their electron wave functions, which can
be considered as overlapping of their electron clouds, causes either attractive or
repulsive forces. The forces will be attractive when the overlap reduces their total
energy, and the forces will be repulsive when the Pauli exclusion principle is in
play. The attractive short-range forces are in the range of 0.5–1 nN per pair of
interactive atoms between a typical tip and a sample. The decay length of the forces
is in the range of 0.05–0.2 nm, larger than that of a tunneling current. In any case,
the variation of the short-range forces on the atomic scale makes the AFM capable
of obtaining topographic images of atoms.
5.3.1.2 van der Waals Forces
The van der Waals forces are the interactive forces between dipoles of molecules.
The dispersion force, a type of van der Waals force between dipoles that arises from
thermal fluctuation or electric-field induction, is always present between molecules.
The van der Waals forces (F v dW ) between tip and sample can be estimated by the
following equation, if we assume the tip is a sphere with radius, R
FvdW =
HR
6d2
(5.2)
H is the Hamasker constant and is in the order of 10− 19 J and d is the spacing
between tip and sample. For a tip radius of 30 nm and vacuum gap of 0.5 nm, the
van der Waals forces are around 2 nN.
The van der Waals forces are significantly affected by the medium of the gap
between tip and sample. For example, when the medium is water rather than
a vacuum, the forces will be greatly reduced because the dielectric constant and
refractive index of water are closer to those of a solid than of a vacuum.
5.3.1.3 Electrostatic Forces
Electrostatic forces refer to the interactive forces between the electric charges of tip
and sample. The charges can be easily trapped at a sample surface and at a tip if
they are insulated. Electrostatic forces can also act between a conductive sample
and a tip if there is an electric potential difference. The electrostatic forces can be
estimated by the follow equation if the spacing between a tip and a sample is small
R
Fels = π εo (Vbias − Vcpd )2
d
(5.3)
ε o is permittivity of vacuum, V bias is the bias voltage applied between tip and
sample, and V cpd represents the contact potential difference due to the difference
in work functions of the tip and the sample. For a tip radius of 20 nm and a distance
171
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5.3 Atomic Force Microscopy
5 Scanning Probe Microscopy
between sample and tip (d) of 0.5 nm, the electrostatic force is about 0.5 nN when
the difference between V bias and V cpd equals 1 V.
We, however, should know that the electrostatic force is considered as long range
compared with the short-range atomic force. The force is proportional to d− 2 as
described by Coulomb’s law, not proportional to d− 1 as shown in Eq. (5.3).
5.3.1.4 Capillary Forces
Capillary forces are forces resulting from water vapor condensation between tip
and sample. In an air environment, water vapor is likely to form a condensed
nucleus there. The water nucleus condensed between tip and sample will form a
meniscus, as schematically shown in Figure 5.6, similar to the water surface in a
capillary tube. The capillary force on the tip can be estimated
Fcap =
4 π Rγ cos θ
1 + d/[R(1 − cos φ)]
(5.4)
γ is the surface tension of a water nucleus. The meanings of angles θ and φ, and
d and R are indicated in Figure 5.6. For a tip radius of 100 nm, the maximum
capillary force reaches about 90 nN. This force is significantly larger than other
forces being discussed. If an attractive force of the order of 10− 8 to 10− 7 N is
recorded, it most likely arises from the capillary. Capillary forces play an important
role in AFM measurements in air. We can reduce these forces by covering the
sample with hydrophobic molecules. AFM measurements in liquid are not affected
by capillary forces.
5.3.2
Force Sensors
The key element of the AFM, or the main difference in structure from the STM,
is its microscopic force sensor. The most common force senor is a cantilever.
The tip is mounted at the end of a cantilever, as shown in Figure 5.7. The force
detection is based on a beam-deflection method. The force between the tip and
sample generates elastic bending of the cantilever. The amount of bending is
monitored and recorded by position-sensitive photodiodes that are arranged in
four quadrants. The photodiodes receive the laser beam reflected from the rear
side of the cantilever, which often has a thin metal coating, making it a mirror.
Any small deflection of the cantilever will tilt the laser beam and change its
Tip
θ
R
φ
d
Sample
Figure 5.6 Capillary force between the tip and sample due
to water formation between them.
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172
A-B
C-D
w
l
x
t
h
Figure 5.7 Detection of cantilever deflection by a laser beam reflected from
the rear side of the cantilever. The reflection is measured by four-quadrant photodiodes. Cantilever deflection is converted to the change in beam position by
photodiodes. t, l, and w, cantilever dimensions; h, distance from back of cantilever
to probe tip. (Reproduced with kind permission of Springer Science and Business
Media from Ref. [1]. © 2004 Springer-Verlag
GmbH.)
striking position on the photodiodes. The difference between the two photodiode
signals indicates the amount of cantilever deflection. The amount of deflection,
in turn, can be mathematically converted into the force on the tip, according to
the elastic properties of the cantilever. The distance between the cantilever and
the photodiodes is about three orders of magnitude greater than the length of the
cantilever. Such an optical arrangement can greatly magnify the tip motion and
provide extremely high sensitivity. Other methods have been used for detecting
cantilever deflection, such as interferometry and piezoelectricity. The photodiode
arrangement, however, is most commonly used because it is inexpensive, easy to
use, and acceptably accurate.
There are two types of cantilever: single beam (Figure 5.8) and triangular beam
(Figure 5.9). A single-beam cantilever beam is usually made from silicon with
dimensions of about 100–500 μm length and 0.5–5 μm width. The triangular
beam is commonly made from silicon nitride. Most cantilevers are produced
with integrated tips in a microfabrication process, similar to the process for
manufacturing integrated circuits in the electronics industry. Such a tip can be
envisaged as a cone with an opening angle and a finite radius at the apex. The apex
radius and open-angled tip shape are crucial parameters for controlling the AFM lateral resolution. A tip radius of about 20 nm has been achieved. The open angle, however, is often limited by the etching characteristics of crystalline materials. Etched
surfaces of crystalline materials are often comprised of certain crystallographic
173
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5.3 Atomic Force Microscopy
5 Scanning Probe Microscopy
15KV
Figure 5.8
4000×.
10 μm
x950 25 mm
15KV
1 μm
x4,000 25 mm
SEM micrographs of a single beam with integrated tip: (a) 950× and (b)
15KV
10 μm
x550 25 mm
1 μm
Figure 5.9 SEM micrographs of a triangular silicon nitride cantilever with integrated tip:
(a) 550× and (b) higher magnification view.
planes. For example, the silicon tip pointing to the 100 direction has a cone angle
of about 54.7◦ , which is the angle between {100} and {111} planes, because {111}
planes are the etched surfaces of crystalline silicon.
5.3.3
Operational Modes
Generally, the operational modes in an AFM can be divided into static or dynamic
modes. In static modes, the cantilever statically deflects to a certain degree and
the feedback loop maintains this set value of deflection during scanning. In
the dynamic modes, the cantilever oscillates at a designated frequency, and the
feedback loop tries to maintain a set value of amplitude of oscillation during
scanning. In static modes, the tip on the cantilever physically ‘‘touches’’ the surface
to be examined. Thus, static modes must be of a contact type. The dynamic modes
include both contact and noncontact types. The most widely used dynamic mode is
the intermittent contact mode, also called the tapping mode. The tapping mode reduces
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174
Tip
(b)
Force
Force
Sample
(a)
z
(c)
A
Distance
z
F/k
(d)
Figure 5.10 Interaction forces between a tip
and sample atoms in: (a) noncontact mode
and (b) contact mode. Force versus distance
between the tip and sample in: (c) noncontact mode and (d) contact mode. The solid
line marks the total force between tip and
sample; dashed line marks short-range force;
A, oscillation amplitude of the tip; arrows
mark the jump-in and spring-off contact in
the static mode; and the straight broken
line marks the value of cantilever spring
constant (k). (Reproduced with kind permission of Ref. [1]. © 2004 Springer-Verlag
GmbH.)
possible damage to a sample during scanning and also can provide information on
chemical and physical properties of the surface, in addition to topography.
Figures 5.10a and b illustrate the difference between interaction forces in contact
and noncontact modes. In the noncontact mode (Figure 5.10a), all forces between
tip and sample are attractive, and the short-range force between the outermost
atoms of tip and sample atoms makes a significant contribution to imaging. In the
contact mode (Figure 5.10b), a repulsive force occurs between tip apex atoms and
the surface atoms, even though the total force is still attractive.
The difference between the static and dynamic modes can be illustrated using
a graph of force versus distance between the tip and a sample. In Figures 5.10
c and d, solid lines represent the total force and the dashed lines represent the
short-range force. The dynamic mode uses stiff cantilevers, while the static mode
uses soft cantilevers. Figure 5.10 c illustrates a case of dynamic mode. The closest
distance between the tip and the sample is marked as z, where the situation is
comparable to that illustrated in Figure 5.10a. The arrow marked A indicates the
typical amplitude of tip oscillation. The closest distance is the turning point of force
curve in order to prevent the tip from being trapped at the sample surface.
Figure 5.10 d illustrates a case of contact mode. The contact position (z) is on the
repulsive side of the short-range force curve. The arrow pointed to the left on Figure
5.10 d represents the phenomenon of tip jump-to-contact with the sample caused
by cantilever elastic bending when the tip is brought near to the surface. The arrow
pointed to the right represents the phenomenon of tip jump-off-contact caused by
elastic recovery of the cantilever when the tip is retracted from the surface. The
phenomena of jump-to and jump-off are characteristics of cantilever behavior in
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5.3 Atomic Force Microscopy
5 Scanning Probe Microscopy
Fext = kN
Δz
Frep
Fattr
Figure 5.11 Force balance in the contact mode. The attractive long-range forces (F attr ) are
balanced by the short-range repulsive force (F rep ) at the contact area and the spring force
of the cantilever. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 2004 Springer-Verlag GmbH.)
the contact mode. The ‘‘jump positions’’ on the force curve depend on the spring
constant of the cantilever (k).
5.3.3.1 Static Contact Modes
The static contact mode is often simply called the contact mode. In this case, the tip
is brought in contact with a sample surface and the cantilever is constantly deflected
during scanning, as schematically shown in Figure 5.11. The tip apex is brought
into the region of a repulsive force, while the rest of the tip experiences attraction to
the sample. The cantilever force, proportional to the vertical deflection, will balance
with forces on the tip. The short-range repulsive force experienced on the tip apex is
most sensitive to topographic features of a sample. Thus, this short-range force will
provide high-resolution images of topography. A three-dimensional topographical
map of the surface can be constructed by plotting the local sample height versus
the horizontal position of the tip.
The resolution of the contact mode depends on a contact area at the tip apex. The
contact diameter (a) can be estimated with the Hertz model in which the contact
area increases with applied force (F) on the tip due to elastic deformation between
tip and sample
a = 2(DRF)1/3
(5.5)
where R is tip radius and D represents the combined elastic properties of the tip
and the sample.
D=
1 − νt2
1 − νs2
+
Et
Es
(5.6)
With Young’s modulus of the tip (E t ) and surface (E s ) in the order of
1.5 × 1011 Nm− 2 , R of 90 nm and applied F in the range 1–100 nN, a will be several
nanometers. v is Poisson’s ratio. This is not small enough to resolve an atomic
image. The contact area diameter can be reduced further in ultrahigh vacuum
and in liquids because long-range forces between tip and sample are reduced.
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176
Figure 5.12 Detection of distortion of the cantilever due to lateral force between tip and
sample in the lateral force microscope. (Reproduced with permission from Ref. [3]. © 2004
Humana Press.)
Nevertheless, in general, it is difficult to obtain atomic resolution with the contact
mode.
5.3.3.2 Lateral Force Microscopy
Lateral force microscopy (also called friction force microscopy) is a variation of the
static contact mode. When the cantilever moves in the lateral direction across
the sample surface during scanning, the friction force between tip and sample
will generate a lateral force on the cantilever and will distort it, as illustrated
in Figure 5.12. The degree of cantilever torsion will be detected by the fourquadrant photodiodes and converted to image signals for lateral force contrast. The
measurement of torsion provides friction characteristics of microscopic surface
areas with a high resolution. Lateral force microscopy also characterizes the friction
as a function of tip velocity moving on the surface. The lateral force contrast cannot
only be generated by friction variation but also by geometric features, such as steps
and holes. The contrast may even be generated by the local variation of normal
force due to the chemical inhomogeneity of materials.
5.3.3.3 Dynamic Operational Modes
Several dynamic modes have been developed to overcome the limits of static
contact modes. The dynamic modes include noncontact, intermittent contact
(tapping mode), and contact types. The dynamic contact mode is also called force
modulation and is described in this section.
Dynamic Noncontact Mode This mode is often simply called the noncontact mode.
This mode can provide true atomic resolution and image quality comparable to
an STM. The cantilever is excited by the piezoactuator to oscillate at or near
its resonant frequency. The vibrating tip is brought near a sample surface, but
not touching the surface, to sense the weak attractive force between tip and
sample instead of the strong repulsive force in the contact mode. As illustrated in
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5.3 Atomic Force Microscopy
5 Scanning Probe Microscopy
Figure 5.13 The dynamic noncontact mode. The frequency shift of the cantilever oscillation
is used to operate the feedback loop. (Reproduced with permission from Ref. [3]. © 2004
Humana Press.)
Figure 5.14 The tapping mode. The oscillation of the cantilever is dampened when the tip
touches the sample surface at each cycle. The image is formed by keeping the oscillation
amplitude constant. (Reproduced with permission from Ref. [3]. © 2004 Humana Press.)
Figure 5.13, the interactions between the tip and the sample shift the oscillation
frequency. The frequency shift signals are used to control the tip–sample distance.
The interaction forces detected in the noncontact mode provide excellent vertical
resolution. However, this mode cannot be operated in a liquid environment. Even
in air, liquid attached on the tip can cause failure in operation.
Tapping Mode This mode is an intermittent contact mode in which the cantilever
oscillates and brings the tip to lightly touch the surface to provide high resolution
and then lifts the tip off the surface to avoid surface damage, as illustrated
in Figure 5.14. As the oscillating cantilever begins to intermittently contact the
surface, the cantilever oscillation amplitude is reduced due to energy loss caused
by the tip contacting the surface. The reduction of oscillation amplitude from the
amplitude in the free-oscillation state can be used to identify and measure surface
features. During operation, the oscillation frequency is maintained constant by a
feedback loop. Selection of the optimal oscillation frequency of the cantilever is
done by computer software. The tip force on the sample is automatically set and
maintained at the lowest possible level. When the tip passes over a bump in the
surface, the cantilever has less room to oscillate and the amplitude of oscillation
decreases. Conversely, when the tip passes over a depression, the cantilever has
more room to oscillate and the amplitude increases (to approach the maximum
free-air amplitude). The oscillation amplitude of the tip is measured by the detector
and input to the controller electronics. The digital feedback loop then adjusts the
tip–sample distance to maintain constant amplitude and force on the sample.
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178
The tapping mode inherently prevents the tip from sticking to the surface and
from damaging the sample surface during scanning. Unlike the contact mode, in
this mode when the tip contacts the surface, it has sufficient oscillation amplitude
to overcome the tip–sample adhesion forces. Further, the surface material is
not pulled sideways by shear forces since the applied force is always vertical.
This is particularly important for soft samples such as polymers and biological
materials.
Phase imaging is a powerful extension of the tapping mode that provides
nanometer-scale information about surface structures often not revealed by other
SPM techniques. By mapping the phase of the cantilever oscillation during the
tapping-mode scan, phase imaging goes beyond simple topographical mapping. It
can detect variations in properties including composition, adhesion, friction, and
viscoelasticity.
In phase imaging, the phase lag of the cantilever oscillation relative to the signal
sent to the cantilever’s piezoelectric actuator is simultaneously monitored and
recorded as illustrated in Figure 5.15. The phase lag is very sensitive to variations in
material properties such as adhesion and viscoelasticity. Once a force microscope
is engaged in the tapping mode, phase imaging is enabled simply by displaying a
second image and selecting the phase data type in software. Both the topography
and phase images are viewed side-by-side in real time. Phase imaging can also act
as a technique to enhance real-time contrast of topographic images, because phase
imaging highlights edges and is not affected by large-scale height differences.
Thus, it provides clear observation of fine features such as grain edges, which can
be obscured by rough topography.
Phase
Force Modulation Force modulation imaging is the dynamic contact mode that
identifies and maps differences in surface stiffness or elasticity. These techniques use a variety of surface properties to differentiate among materials where
topographical differences are small or not measurable.
In the force-modulation operation, a low-frequency oscillation is induced (usually
large enough to bring the tip in contact with the sample); when the tip contacts the
sample, a constant force on the sample is applied. The cantilever deflection during
Figure 5.15 Phase image in the tapping mode. The phase lag of cantilever oscillation is
detected. The phase lag is very sensitive to variations in material properties such as adhesion and viscoelasticity.
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5.3 Atomic Force Microscopy
5 Scanning Probe Microscopy
Figure 5.16 Force modulation. The tip is kept in contact with the sample. Differences in
local properties of the sample will be reflected in the amplitude change of the cantilever.
(Reproduced with permission from Ref. [3]. © 2004 Humana Press.)
scanning is recorded. Under the same applied force, a stiffer area on the sample
will undergo less elastic deformation than a soft area. Thus, a stiffer area generates
greater resistance to the vertical oscillation and less bending of the cantilever,
as illustrated in Figure 5.16. The variation in cantilever deflection amplitude is
a measure of the relative stiffness of the surface. Topographical information is
collected simultaneously with the force-modulation data.
5.3.4
Typical Applications
5.3.4.1 Static Mode
The static contact mode is the simplest mode to use for obtaining basic topographic
information of solid surfaces. Figure 5.17 is an image of surface crystalline
polyethylene obtained with the contact mode. The contact mode was able to detect
the nanoscale roughness of crystalline polyethylene, which is believed to be chain
folds of polyethylene. The scale of the topography in Figure 5.17 implies that
the primary function of an AFM is not the same as a surface profiler for surface
roughness measurement. This means that AFM samples should have limited height
variations on their surfaces, usually less than 1 μm, because vertical movement
of the scanner is limited. Interpretation of AFM images such as Figure 5.17 also
10
0.50
0.25
5
0
0
nm
5
10
Figure 5.17 Topography of crystalline polyethylene. The chain folds of the crystal structure generate the rough appearance. (Reproduced with permission from Ref. [4]. © 1998
American Chemical Society.)
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180
(a)
(b)
Figure 5.18 A scanning force microscope
(SFM) image (5 μm × 5 μm) of a mixed film
of fluorocarbon and hydrocarbon carboxylates. The circular domains were assigned
to the hydrocarbon component and the surrounding flat film to the partially fluorinated
component: (a) topographic image and (b)
lateral force image obtained simultaneously
with the topography. The measured lateral
force generates higher contrast due to the
difference in friction. (Reproduced with permission from Ref. [2]. © 1994 Cambridge
University Press.)
relies on knowledge of the tip being used because the tip apex size determines
the resolution of the topography. The distortion of topography due to a blunt
tip might have hindered revealing the polymer chain folds protruding from the
surface.
Lateral force microscopy, as one type of contact mode, can generate contrast
in an image from geometrical features such as surface steps and holes because
such features change local friction. More importantly, contrast can be generated
by materials whose surface properties vary. For example, Figure 5.18 shows lateral
force contrast on a film consisting of two types of polymers. Comparing the two
images in Figure 5.18, we realize the difference between material-specific contrast
and topographic contrast.
There has been a general trend since the mid-1990s for the static contact mode for
surface topography to be gradually replaced by the dynamic noncontact or tapping
modes, except for materials examined in a liquid environment. The dynamic
modes provide better image resolution and are less likely to damage the sample
surface.
5.3.4.2 Dynamic Noncontact Mode
The dynamic noncontact mode can provide atomic resolution in an ultrahigh
vacuum, even though it is more difficult to generate an atomic image with an AFM
than with an STM. Figure 5.19 shows an example of atomic resolution imaging
with a noncontract mode. The hydrogen atoms absorbed on the Si (100) surface in
an ultrahigh vacuum of 2 × 10− 8 Pa are revealed as the bright spots in Figure 5.19.
The interaction between the hydrogen atom on the topmost layer and the silicon
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5.3 Atomic Force Microscopy
5 Scanning Probe Microscopy
0.35 ± 0.01 nm
2 nm
ca.3 Hz
6 Hz
3.4 nm
Figure 5.19 A noncontact mode image
of a hydrogen-terminated silicon monohydride surface. Line profile of frequency
shift along the white dotted line indicates the location of hydrogen atoms. The
initial frequency of the cantilever is about
3 Hz. (Reproduced with kind permission
of Springer Science and Business Media from Ref. [5]. © 2002 Springer-Verlag
GmbH.)
tip apex generates a frequency shift of cantilever oscillation. The frequency-shift
signals were converted to image contrast that reveals the locations of hydrogen
atoms as bright spots.
5.3.4.3 Tapping Mode
The tapping mode is becoming popular for topographic measurements. As an
example, Figure 5.20 shows an image, created in the AFM by tapping mode, of the
topography of a high-speed transistor. The image clearly reveals the multiple layers
of Al x Ga (1 − x) N deposited on a sapphire substrate by metal-organic chemical
vapor deposition (MOCVD) with very precise control.
5.3.4.4 Force Modulation
Force modulation as a dynamic contact mode has the advantage of being able
to distinguish materials with difference elastic properties. For example, Figure
5.21 shows the comparison between topographic and force modulation images
of carbon-fiber-reinforced epoxy. The topographic image reveals the difference in
height of a composite cross section (Figure 5.21a), but it does not provide clear
distinction between the fibers and matrix. The force modulation image (Figure
5.21b), resulting from the elastic stiffness difference between the fibers and matrix,
reveals the location of individual carbon fibers in the cross section of the composite
sample. The high stiffness of carbon fibers compared to epoxy generates high
contrast in the image.
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182
2.00
4.0 nM
2.0 nM
1.0
0.0 nM
0
0
2.00
μM
1.00
Figure 5.20 Tapping-mode image of multiple layers of Al x Ga (1 − x) N deposited on a sapphire substrate. (Reproduced with permission of Kei May Lau.)
(a)
(b)
Figure 5.21 Cross section of carbon fibers in an epoxy matrix: (a) topographic image and
(b) force-modulation image. The image width is 32 μm. (Reproduced with permission from
Ref. [2]. © 1994 Cambridge University Press.)
5.4
Image Artifacts
While SPM offers unique advantages for surface measurement in terms of simplicity and high resolution, it also has its unique problems of image artifacts
caused by near-field interactions between tip and sample. The artifacts in imaging
may originate from the tip, the scanner, vibrations, and/or image processing.
Typical artifacts as introduced from several sources are briefly described in this
section.
183
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5.4 Image Artifacts
5 Scanning Probe Microscopy
5.4.1
Tip
The geometry of the tip can generate artifacts. In SPM operation, the tip either
contacts or nearly contacts the sample surface. The sharpness of the tip affects the
mapping of the sample surfaces unless the tip is sharper than the surface features
being mapped. Two geometrical parameters of the shape of the tip that are relevant
here are tip apex and sidewall angle (also called the opening angle) of the tip.
The tip geometry may alter the lateral dimension of surface features in an image.
For example, if a surface feature has a sharper edge than the tip’s sidewall angle,
the image of the surface feature will be distorted in its lateral direction because
the imaged edge cannot be sharper than the sidewall angle. For a small surface
protrusion, the image size could be larger than the real feature as illustrated in
Figure 5.22a. When the tip maps a surface pit or hole, the sidewall angle and size
of the tip apex may prevent the tip from reaching the bottom of the pit or hole.
Consequently, the image of the pit or hole would be shallower and smaller than
the real feature, as illustrated in Figure 5.22b.
The tip geometry may also cause double imaging when the tip does not have a
single apex. When the size of a surface feature is significantly smaller than the tip
radius, such as a nanoscale particle, two protrusions on one tip can physically map
the feature twice and generate two images of one feature, as illustrated in Figure
5.23. Ideally, the tip apex for atomic-scale imaging should be a single atom. A tip
with two or more atomic apices is more practically possible.
Tip artifacts may also result from a damaged tip or a tip contaminated by debris.
For example, when a damaged tip maps a surface feature with lateral symmetry
(a)
(b)
Figure 5.22 Artifacts generated by tip: (a) the side of tip causes broadening of the image
of the protruding object and (b) the width of the tip causes distortion of the hole geometry
in the image. (Reproduced with permission from Ref. [3]. © 2004 Humana Press.)
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184
Figure 5.23 Image distortion by a tip with a double apex. (Reproduced with permission
from Ref. [3]. © 2004 Humana Press.)
Figure 5.24 Image distortion by a damaged tip. (Reproduced with permission from
Ref. [3]. © 2004 Humana Press.)
(such as an etched pit), the tip will generate an asymmetric image profile, as
illustrated in Figure 5.24. A tip with contaminating debris can cause image contrast
changing and blurring during surface mapping.
5.4.2
Scanner
The scanner controlling the tip position and tip scanning is made from piezoelectric materials. The intrinsic physical and mechanical properties of piezoelectric
materials, such as nonlinear piezoelectricity, hysteretic piezoelectricity, and creep
deformation affect the performance of the scanner. Such properties can generate
distortion of SPM imaging during scanning.
The relationship between the electric voltages applied to the scanner and the
scanner extension is not perfectly linear (the piezoelectric coefficient is not truly
constant). Consequently, an image may be distorted in its lateral dimensions. The
nonlinearity effects should be of concern when the lateral scanning range is greater
than 100 μm. Nonlinear distortion can be revealed by imaging a surface grid with
periodic structure, as illustrated in Figure 5.25. Such a grid pattern can be used to
calibrate the linearity of a scanner. The nonlinearity of the scanner has less effect on
measurement in the vertical direction because the vertical movement of the scanner
is about one order of magnitude smaller than its lateral movements. The SPM is
commonly equipped with linearity corrections made by either software or hardware.
The hysteretic behavior of piezoelectric materials is similar to the hysteretic
behavior of magnetic materials. It occurs because there is an electrical voltage
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5.4 Image Artifacts
5 Scanning Probe Microscopy
(a)
(b)
Figure 5.25 Image distortion caused by nonlinearity of the piezoelectric scanner: (a) regular grid and (b) distorted image of grid. (Reproduced with permission from Ref. [3]. © 2004
Humana Press.)
Figure 5.26 Hysteresis effects of a piezoelectric scanner on imaging. The bottom figure illustrates the profile difference between forward and backward scanning. (Reproduced with
permission from Ref. [3]. © 2004 Humana Press.)
difference for scanner elongation in the forward and backward directions. Thus,
the tip may not return to its original position after one voltage loop applied to
the scanner. The tip position can deviate by as much as 15% between forward
and backward scanning. Image distortion caused by the hysteretic properties of
the scanner can be illustrated by comparing surface profiles obtained by forward
and backward scanning, as shown in Figure 5.26. The hysteresis of the scanner
generates a lateral shift between two profiles.
Creep deformation causes the scanner to show time-dependent extension. Creep
deformation of the scanner will extend its length with time at a constant voltage.
The profile of surfaces can be different between a first scan and a second scan,
after a certain period of applying a voltage. Creep in the vertical direction leads to
‘‘overshoot’’ of the scanner position at the leading and trailing edges of surface
features in slow scanning (Figure 5.27). Consequently, the images will have a
shaded edge in a lateral direction.
Thermal drift also can cause instability of the mapping surface. Thermal drift
refers to the effect of temperature change on the scanner. Thermal drift may
come from the applied electrical power and the SPM working environment.
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186
Figure 5.27 Creep effects of a piezoelectric scanner on image topography. In slow scanning, the ‘‘overshoot’’ of the scanner occurs at two edges of a surface feature. (Reproduced
with permission from Ref. [3]. © 2004 Humana Press.)
High-resolution imaging is likely to be affected by a fraction of a degree change in
temperature. Thus, it is advisable to have a waiting period for SPM operation and
for control of environments.
5.4.3
Vibration and Operation
As aforementioned, the SPM requires excellent vibration isolation. Artifacts in
images can be generated by floor vibration as well as acoustic vibration. Artifacts
due to vibration appear as oscillation patterns in images. The floor can vibrate in
the vertical direction with a magnitude of several micrometers and at a frequency
less than 5 Hz. SPM operation can be affected even by people walking in a hallway.
While a good vibration insulation system should be installed, even better insulation
is achieved if the SPM system is placed on the ground floor of a building, and
ideally at a corner of a room. The SPM can be insulated from acoustic vibration
caused by talking and music by the installation of an acoustic hood.
Artifacts can also be generated by inappropriately selected operational parameters
including the feedback-loop control, oscillation parameters of the AFM cantilever
and scan speed. Setting appropriate parameters for operation relies primarily on an
operator’s experience; however, there are several general guidelines we can follow.
The gain parameter of the feedback loop determines the sensitivity of control over
the surface features. A high-gain parameter may cause scanner-system oscillation
and may generate high-frequency noise in an image. A low-gain parameter can
ensure that the tip tracks the surface topography, and thus, the surface features
are not smeared out. Soft samples should be scanned at low scanning speed and
with low interaction forces in the AFM. Rough samples also need a low scanning
speed.
There are several ways to detect possible artifacts in images:
•
•
•
•
•
repeat the scan for the same area;
change the scanning direction;
change the scanned area size;
rotate the sample and conduct a second scan; and
change the scanning speed.
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5.4 Image Artifacts
5 Scanning Probe Microscopy
Artifacts are most likely to be revealed if the image changes after changing such
scanning methods.
Questions
5.1 Is it practical to measure the topography of a 1-mm × 10-mm area with an
SPM? Give your reasons.
5.2 Is it practical to measure the topography of a sample with roughness z > 10
μm? Why?
5.3 What characteristics of a tunneling current enable it to be used for imaging
atoms?
5.4 Why is an ultrahigh vacuum environment often necessary for operation of
an STM?
5.5 A hole appears in an STM image with atomic resolution. Can we assume it
is an atomic vacancy? Why?
5.6 Can you examine a polymer sample with STM? Why?
5.7 Why, in your opinion, are people more likely to use an AFM than an STM
for topographic examinations?
5.8 What are the typical levels of the short-range force, the van der Waals force
and the electrostatic force, respectively?
5.9 To obtain atomic resolution, the force between the sample and tip of an
AFM should decay significantly at a distance of atomic spacing. Plot the van
der Waals force as a function of distance between the tip and sample and
the tip radius using Eq. (5.2). Can we obtain atom images with the van der
Waals force?
5.10 Estimate the capillary force between the tip and sample using Eq. (5.4),
and compare the level of maximum capillary force with the van der Waals
force estimated in Problem 5.9. Assume the surface tension of water
γ = 0.074 Nm− 1 at 20 ◦ C.
5.11 What is the typical level of a capillary force? How can you eliminate the
capillary force during your AFM operation?
5.12 Compare the contact areas in contact mode using Eq. (5.5): (i) a silicon
tip with an iron sample and (ii) a silicon tip with a polymer sample.
Assume that the contact force is 10 nN and radius of the tip is 80 nm;
the Young’s moduli of tip, iron, and polymer are about 0.17 × 1012 ,
0.2 × 1012 , and 0.1 × 1012 Nm− 2 , respectively; and their Poisson ratio is
about 0.3.
5.13 What are advantages of the tapping mode comparing with the static contact
mode for AFM topographic examination?
5.14 What is the difference in operating tip between the tapping mode and the
force modulation?
5.15 Is there any way, not using a standard grid, to check whether there is
nonlinearity in the scanner? Explain.
5.16 Suggest methods to check possible damage on a tip.
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188
References
1. Meyer, E., Hug, H.J., and Bennewitz, R.
5. Morita, S., Wiesendanger, R., and Meyer,
(2004) Scanning Probe Microscopy: The Lab
E. (eds) (2002) Noncontact Atomic Force
on a Tip, Springer-Verlag, Berlin.
Microscopy, Springer-Verlag, Berlin.
2. Wiesendanger, R. (1994) Scanning Probe
Microscopy and Spectroscopy, Cambridge
University Press, Cambridge.
Further Reading
3. Braga, P.C. and Ricci, D. (eds) (2004)
Atomic Force Microscopy, Humana Press,
Birdi, K.S. (2003) Scanning Probe Microscopes,
Totowa, NJ.
CRC Press, Boca Raton, FL.
4. Ratner, B.D. and Tsukruk, V.V. (eds)
Wiesendanger, R. (ed) (1998) Scanning Probe
(1998) Scanning Probe Microscopy of
Microscopy, Springer, Berlin.
Polymers, American Chemical Society,
Washington, DC.
189
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Further Reading
6
X-Ray Spectroscopy for Elemental Analysis
X-ray spectroscopy is a technique of using characteristic X-rays to identify chemical
elements; it is to be distinguished from X-ray diffraction for crystal structure
analysis. X-ray spectroscopy determines presence and quantities of chemical elements by detecting characteristic X-rays that are emitted from atoms irradiated by
a high-energy beam. From the characteristic X-rays emitted from sample atoms,
chemical elements can be identified either from the X-ray wavelength, as in X-ray
wavelength dispersive spectroscopy (WDS) or from the X-ray energy, as in X-ray
energy dispersive spectroscopy (EDS). The most commonly used spectrometers
for X-ray spectroscopy include X-ray fluorescence (XRF) spectrometers and microanalyzers in electron microscopes (EMs). The XRF spectrometer is a standalone
equipment for elemental analysis. It uses X-ray radiation to excite the emission
of characteristic X-rays from sample atoms. The word ‘‘fluorescence,’’ is used to
distinguish the secondary X-ray emission of sample atoms from the primary X-rays
irradiating the sample. A microanalyzer is an EDS type of X-ray spectrometer that
is commonly found in a scanning or a transmission electron microscope (TEM).
The EDS microanalyzer in an EM that uses a primary electron beam to excite the
emission of characteristic X-rays from the sample atoms. Since the electron beam
can be readily focused on a microscopic area on a sample, the EDS microanalyzer
can examine chemical compositions in a microscopic area; while the XRF spectrometer is mainly used to examine overall chemical compositions in a sample.
This chapter introduces both XRF spectrometers and microanalyzers in EMs.
6.1
Features of Characteristic X-Rays
Characteristic X-rays were introduced in Chapter 2 when discussing monochromatic X-ray radiation for the X-ray diffractometer. It is necessary, however, to
further discuss the features of characteristic X-rays in this chapter because they are
the essential signals used in X-ray spectroscopy for identifying chemical elements.
Figure 6.1 schematically illustrates the generation of characteristic X-rays when
an atom is irradiated by high-energy particles. When a high-energy particle, such
as an X-ray photon, an electron, or a neutron, strikes an electron in the inner shell
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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191
6 X-Ray Spectroscopy for Elemental Analysis
Incident electron
or photon
M
Electron shell
L
K
Scattered primary
electron
Ejected orbital
electron
M
L
Atomic nucleus
Electron
K
Electron relaxation
and photon generation
Vacancy
M
M
L
K
Photon internally
converted and
Auger electron
emitted
L
K
X-ray photon emitted
Figure 6.1 Excitation of a characteristic X-ray photon or an Auger electron by a high-energy
X-ray photon or electron.
of an atom, the energy of the particle can be high enough to knock an electron out
of its original position in an atom. The knocked-out electron leaves the atom as
a ‘‘free’’ electron and the atom becomes ionized. Because ionization is an excited
state, the atom will quickly return to its normal state after refilling the inner
electron vacancy by an outer shell electron. In the meantime, the energy difference
between an outer-shell electron and an inner-shell electron will generate either an
X-ray photon (characteristic X-ray) or another characteristic free electron that is
emitted from the atom. The latter is called an Auger electron, which also can be used
for elemental analysis (this will be discussed in Chapter 7).
The energy of characteristic X-rays is the energy difference between two electrons
in different shells. It is well defined and dependent on the atomic number of the
atom. For example, the energy of the X-ray Kα line is the energy difference between
a K shell electron and L shell electron. Thus, we can identify a chemical element
from the characteristic X-rays that it emits. Moseley’s Law defines the relationship
between wavelength of characteristic X-rays (λ) and atomic number (Z)
B
(6.1)
λ=
(Z − σ )2
B and σ are constants that depend upon the specific shells. This relationship can
also be expressed as the energy of characteristic X-rays and atomic number using
the energy–wavelength relationship (Eqs. (9.1) and (9.4)).
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192
6.1.1
Types of Characteristic X-Rays
A number of characteristic X-rays can be emitted from an atom if a number of
inner-shell electrons have been knocked out by high-energy particles. The individual
characteristic X-rays are marked Kα, Kβ . . . as mentioned in Chapter 2. It seems
that there are many possible ways in which outer-shell electrons can fill inner-shell
vacancies; however, the possibilities are limited and such electron transitions in an
atom are controlled by the selection rules.
6.1.1.1 Selection Rules
Each electron in an atom is defined by four quantum numbers: n, l, m, and s. The
principal quantum number (n) defines the shell; for example, the K shell as 1,
L shell as 2, and the M shell as 3. The angular quantum number (l) defines the
number of subshells, taking all values from 0 to (n − 1). The magnetic quantum
number (m) defines the number of energy states in each subshell, taking values − l,
0, and + l. The spin quantum number (s) defines two spin moments of electrons
in the same energy state as + 12 and − 12 . The quantum numbers of electrons in K,
L, and M shells are listed in Table 6.1. Table 6.1 also gives the total momentum
(J), which is the sum of (l + s). No two electrons in an atom can have same set
quantum numbers (n, l, m, s).
Selection rules for electron transitions between two shells are as follows:
1) change in n must be at least 1 (n ≥ 1);
2) change in l must be 1 (l = ±1); and
3) change in J must be either 0 or 1 (J = ±1, or 0).
Table 6.1
Electron structure and quantum numbers in K, L, and M shells.
Shell (electrons)
n
l
m
s
K (2)
L (8)
1
2
2
2
2
3
3
3
3
3
3
3
3
3
0
0
1
1
1
0
1
1
1
2
2
2
2
2
0
0
1
0
−1
0
1
1
−1
2
1
0
−1
−2
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
± 12
M (18)
Orbitals
J
1s
2s
1
2
1
2
2p
1 3
2; 2
3s
1
2
3p
1 3
2; 2
3d
3 5
2; 2
193
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6.1 Features of Characteristic X-Rays
6 X-Ray Spectroscopy for Elemental Analysis
Characteristic X-rays are divided into K, L, and M series according to the shells
of electron vacancies being filled. For example, ‘‘K series’’ means the characteristic
X-rays emitted when an outer-shell electron fills an electron vacancy in the K shell.
According to the selection rules, the electron transition from the L1 to the K shell
is forbidden because the l change would be zero, which would violate the second
selection rule. Thus, the only possible transitions from the L to K shell are L3
to K and L2 to K, which are known as Kα 1 and Kα 2 , respectively, as mentioned
in Chapter 2. Figure 6.2 shows the example of shell structures of electrons and
the possible characteristic X-rays emitted when an electron transitions to a K, L,
or M shell in barium with atomic number of 56. Figure 6.2 also shows that the
characteristic X-ray can be classified as K, L, or M series, according to the ground
state of the electron transition. The Siegbahn Notation is commonly used to specify a
characteristic X-ray line. The Siegbahn Notation comprises a capital English letter,
a lower-case Greek letter, and a subscript number.
Generally, the Greek letters indicate the general order of the X-ray intensity,
where the X-ray intensity of α >β >γ . Figure 6.3 illustrates the relative intensities
of Kα and Kβ on top of continuous X-ray radiation. The subscript number also
indicates the relative intensity, with number 1 as the highest.
6.1.2
Comparison of K, L, and M Series
An atom’s ability to generate characteristic X-ray photons varies when it is irradiated
by high-energy X-ray photons or electrons. First, there is an emission competition
between the characteristic X-ray photon and the Auger electron when an electron
refills an inner-shell vacancy. Secondly, there are competitions among generations
5p [OII,III]
5s [OI]
γ
β3 β4 γ2 γ3 γ4 η1 β1 γ1 I α1 α2 β2
4d [NIV,V]
4p [NII,III]
4s [NI]
3d [MIV,V]
3p [MII,III]
3s [MI]
2p [LII,III]
2s [LI]
α1 α2 β1 β2 β3
LI Lines
LII Lines LIII Lines M Lines
1s [K]
K Lines
Figure 6.2
(Z = 56).
Example of allowable electron transitions in K, L, and M shells for barium
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194
Intensity
Kα
Kβ
0.2
0.4
0.6
0.8
Wavelength (Å)
1.0
Figure 6.3 Primary X-ray radiation generated by the X-ray tube, including continuous and
characteristic radiations.
of K, L, and M series of the X-rays. A parameter, fluorescent yield, has been used
to measure the relative effectiveness of X-ray generation. Figure 6.4 shows the
fluorescent yield (ω) variation in K, L, and M series for a range of atomic numbers.
Table 6.2 lists the values of fluorescent yields of some elements in the K, L, and
M series.
For an atom with an atomic number lower than 4 (Be), the fluorescent yield is 0,
and for an atomic number lower than 8 (O), the yield is less than 0.5%. Generally,
the fluorescent yield increases with atomic number, as shown in Figure 6.4. Thus,
there is an intrinsic disadvantage for detection of light elements using X-ray
spectroscopy. Figure 6.4 also indicates that the generation of the K series X-rays
is more effective than the L and M series X-rays. This means that the intensity of
the K series X-rays is always higher than the L series, and in turn, the L series is
always higher than the M series. The fluorescent yield is zero for the L series when
the atomic number is lower than 20 (Ca), and for the M series when the atomic
number is less than 57 (La).
Another difference among the K, L, and M lines is their energy levels (or
wavelengths). The energy of K series is the highest, followed by L and M series,
as shown in Figure 6.5. Table 6.3 lists K, M, and L wavelengths and energies for
selected elements. For example, the energy of Au Kα 1 reaches 66.99 keV, but the
energies of Au Lα 1 and Au Mα 1 are 9.713 and 2.123 keV, respectively. A typical
X-ray energy spectrum is in a range from 0.2 to 20 keV. Thus, the Au Kα 1 will be
absent in such a spectrum. In general, the L and the M lines of heavy elements
are much more likely than their K lines to be detected by an X-ray spectrometer
because the energies of the K lines are likely to be higher than 20 keV. An X-ray
spectrum of a high atomic number element is complicated because of the existence
195
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6.1 Features of Characteristic X-Rays
6 X-Ray Spectroscopy for Elemental Analysis
1.0
K
Fluorescent yield
0.8
0.6
L
0.4
0.2
M
0
20
40
60
Atomic number
80
100
Figure 6.4 Fluorescent yield variation with atomic number and with the K, L, and M characteristic lines.
of X-rays from different series. On the other hand, the spectra of atomic numbers
lower than 20 (Ca) contain only the K lines. The energies of L and M lines for low
atomic numbers, as well as the fluorescent yield, can be too low to be detected in
the X-ray spectrometer.
6.2
X-Ray Fluorescence Spectrometry
XRF analyzes the chemical elements of specimens by detecting the characteristic
X-rays emitted from the specimens after radiation by high-energy primary Xrays. The characteristic X-rays can be analyzed from either their wavelengths or
energies. Thus, there are two types of XRF: WDS and EDS. Figure 6.6 schematically
illustrates the structural similarities of, and differences between, WDS and EDS
instruments. An XRF instrument consists of three main parts: the X-ray source,
detection system, and data collection and processing system.
The X-ray source generates the primary X-rays to excite the atoms of specimens.
The most commonly used source is the X-ray tube, similar to that used in the X-ray
diffractometer introduced in Chapter 2. The X-ray tube is operated at a power of
0.5–3 kW and with high voltage of 30–50 kV. The reason for using high voltage is
to ensure that the X-rays impinging the specimen exceed the critical potential of
exciting characteristic X-rays from the elements in specimens. The optimum ratio
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196
Table 6.2
Fluorescent yield of chemical elements.
Atomic number
4
5
6
7
8
9
10
11
12
...
19
20
21
22
23
24
...
56
57
58
59
...
Element
ωK
ωL
ωM
Be
B
C
N
O
F
Ne
Na
Mg
...
K
Ca
Sc
Ti
V
Cr
...
Ba
La
Ce
Pr
...
0.00045
0.00101
0.00198
0.00351
0.00579
0.00901
0.0134
0.0192
0.0265
...
0.138
0.163
0.190
0.219
0.249
0.281
...
0.900
0.906
0.911
0.915
...
—
—
—
—
—
—
—
—
—
...
—
0.00067
0.00092
0.00124
0.00163
0.0021
...
0.126
0.135
0.144
0.153
...
—
—
—
—
—
—
—
—
—
...
—
—
—
—
—
—
...
—
0.00111
0.00115
0.00120
...
Data taken from Ref. [1]. © 1992 Springer Science.
106
EK,L,M (eV)
106
106
106
K
106
106
L
1
10
Atomic number, Z
M
100
Figure 6.5 Energies of characteristic X-ray photons in the K, L, and M lines.
197
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6.2 X-Ray Fluorescence Spectrometry
6 X-Ray Spectroscopy for Elemental Analysis
Table 6.3
Atomic
number
4
5
6
7
8
9
10
11
12
13
14
15
16
17
...
19
20
21
22
23
24
25
26
27
28
29
30
...
45
46
47
56
57
58
59
...
78
79
80
...
Characteristic X-ray wavelengths and energies of selected elements.
Element
Kα 1
λ (Å)
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
...
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
...
Rh
Pd
Ag
Ba
La
Ce
Pr
...
Pt
Au
Hg
...
114
67.6
44.7
31.6
23.62
18.32
14.61
11.91
9.89
8.339
7.125
6.157
5.372
4.728
...
3.741
3.358
3.031
2.749
2.504
2.290
2.102
1.936
1.789
1.658
1.541
1.435
...
0.6133
0.5854
0.5594
0.3851
0.3707
0.3571
0.3441
...
0.1855
0.1851
0.1751
...
Lα 1
Mα 1
E (keV)
λ (Å)
E (keV)
λ (Å)
E (keV)
0.109
0.183
0.277
0.392
0.525
0.677
0.849
1.041
1.254
1.487
1.740
2.014
2.308
2.622
...
3.314
3.692
4.091
4.511
4.952
5.415
5.899
6.404
6.930
7.478
8.048
8.639
...
20.13
21.18
22.16
32.19
33.44
34.72
36.03
...
66.83
66.99
70.82
...
—
—
—
—
—
—
—
—
—
—
—
—
—
—
...
—
36.33
31.35
27.42
24.25
21.64
19.45
17.59
15.97
14.56
13.34
12.25
...
4.597
4.368
4.154
2.776
2.666
2.562
2.463
...
1.313
1.276
1.241
...
—
—
—
—
—
—
—
—
—
—
—
—
—
—
...
—
0.341
0.395
0.452
0.511
0.573
0.637
0.705
0.776
0.852
0.930
1.012
...
2.697
2.839
2.984
4.466
4.651
4.840
5.034
...
9.442
9.713
9.989
...
—
—
—
—
—
—
—
—
—
—
—
—
—
—
...
—
—
—
—
—
—
—
—
—
—
—
—
...
—
—
—
—
14.88
14.04
13.34
...
6.047
5.840
5.645
...
—
—
—
—
—
—
—
—
—
—
—
—
—
—
...
—
—
—
—
—
—
—
—
—
—
—
—
...
—
—
—
—
0.833
0.883
0.929
...
2.051
2.123
2.196
...
Data taken from Ref. [1].© 1992 Springer Science.
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198
Specimen
Detector
θ
2θ
Source
I
Crystal
2θ
(a)
Specimen
Multichannel
analyzer
I
Source
Si(Li) Detector
E
(b)
Figure 6.6 Main components and dispersive spectra of: (a) WDS and (b) EDS.
of tube voltage to the critical potential is about 3–5. The X-ray radiation is produced
by electrons striking a metal target in the tube. The target metals include Cr, Rh,
W, Ag, Au, and Mo. The emitted X-rays from the source consist of both continuous
and characteristic radiations (Figure 6.3).
The main difference between the WDS and EDS instrumentation is in the
X-ray detection systems. The WDS type uses single-crystal diffraction to detect
characteristic wavelengths emitted from the specimen, because, according to
Bragg’s Law, the single crystal is able to diffract a specific wavelength at a
specific angle between the incident X-ray beam and a crystallographic plane. The
EDS instrument uses a photon detector, typically a Si(Li) diode, to separate the
characteristic X-ray photons according to their energies. The features and properties
of the WDS and EDS systems are introduced in the following subsections.
6.2.1
Wavelength Dispersive Spectroscopy
XRF spectrometry was introduced as WDS in the early 1950s; the EDS type came
along years later. WDS provides better resolution and a wider range of elemental
analysis than EDS, although its instrumentation is more complicated. The WDS
systems can resolve relative changes in wavelength ( λ
) in the range 0.002–0.02.
λ
This range corresponds to the energy range 0.01–0.1 keV, which is about 1 order of
magnitude better than that of EDS. Modern WDS systems can detect elements from
upward of C (Z = 6). Figure 6.7 illustrates the structure of a WDS system, which
is similar to an X-ray diffractometer. There is a rotating X-ray detector system (an
analyzing crystal and X-ray photon counter in Figure 6.7) to collect the diffraction
beam, and collimators to align the characteristic X-ray beam from the specimen and
199
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6.2 X-Ray Fluorescence Spectrometry
6 X-Ray Spectroscopy for Elemental Analysis
Sample
Primary beam
filter
Collimator mask
Vacuum seal
Collimator
θ
X-ray tube
Analyzer
crystal
2θ
Photo counter
Figure 6.7 WDS apparatus, which includes the X-ray tube, specimen, primary collimator,
analyzing crystal, flow counter, auxiliary collimator, and scintillation counter.
the beam diffracted from the analyzing crystal. The rotating X-ray photon counter
scans a range of 2θ to detect specific wavelengths of characteristic X-rays from
the specimen. We can understand that the signal detection in WDS is sequential
in nature because of 2θ scanning. A WDS system may have one crystal/detector
set (single channel) or a number of crystal/detector sets (multichannel). The
multichannel system can partially overcome the drawbacks of sequential detection
and increase analysis speed.
6.2.1.1 Analyzing Crystal
In WDS, the analyzing crystal should be carefully selected because it determines
the range of detectable atomic numbers. The wavelength that can be detected by a
crystal is defined by Bragg’s Law.
2d sin θ
(6.2)
n
Normally, the maximum achievable θ angle in a WDS system is about 73◦ .
Thus, the maximum λ of characteristic X-rays being diffracted is about 1.9d of
the analyzing crystal. Table 6.4 lists the commonly used analyzing crystals for
WDS, which include LiF, pentaerythrital (PE), thallium acid phthalate (TAP),
and layered synthetic microstructure (LSM). For detecting light elements, which
have long wavelengths of characteristic X-rays, an analyzing crystal with a large
atomic spacing must be used. For detecting elements with atomic numbers less
than 9, LSM materials with extremely large d-spacings should be used. Although
an analyzing crystal with small d-spacing limits the range of detectable atomic
numbers, the small d-spacing can increase angular dispersion. This can be seen by
differentiating the Bragg’s Law equation.
λ=
n
dθ
=
(6.3)
dλ
2d cos θ
Equation 6.3 implies that we will obtain the wave spectrum of higher resolution
when using a small d-spacing crystal. However, using the analyzing crystal with a
small d will reduce the range of wavelength to be detected because of the 1.9d limit.
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200
Table 6.4
Analyzing crystals used in wavelength dispersive spectrometers (WDS).
Crystal
Lithium fluoride
(LiF)
Lithium fluoride
(LiF)
Pentaerythrital
(PE)
Thallium acid
phthalate (TAP)
Layered synthetic
microstructure
(LSM)
Plane
Plane spacing, 2d (Å)
Atomic number range
K lines
L lines
(220)
2.848
>Ti(22)
>La(57)
(200)
4.028
>K(19)
>Cd(48)
(002)
8.742
Al(13)–K(19)
—
(001)
26.4
Fe(9)–Na(11)
—
—
50–120
Be(4)–F(9)
—
Reproduced with permission from Ref. [2] .© 1999 John Wiley & Sons Inc.
6.2.1.2 Wavelength Dispersive Spectra
A WDS spectrum is presented as a diagram in which the characteristic X-ray lines
are dispersed in a range of the X-ray wavelengths, as shown in Figure 6.8. The
relative intensities of the individual X-ray lines are represented by their heights
in the spectrum; however, there is no scale to indicate the real intensities of the
X-rays. Similar to the spectrum of X-ray diffraction, only relative intensities among
the lines, and with respect to the background, are important. An individual line is
marked with the corresponding element that generates it and its specific line code,
such as CrKα or CrKα 1,2 . The reason is that the wavelength resolution is unable to
separate CrKα 2 from CrKα 1 . Often, we need more than one type of analyzing crystal
to obtain the whole range of wavelength dispersion from a specimen, because the
limitation of wavelength ranges by the crystal’s d-spacing. For example, Figure 6.8
shows the spectra of a nickel-based alloy obtained by LiF and TAP analyzing
crystals. The spectrum obtained with LiF covers a short-wavelength range and
that obtain with TAP covers a long-wavelength range. The two spectra provide a
complete chemical analysis of the nickel-based alloy that contains Cr, Co, W, Ta,
V, Al, and Re. The relative intensities of spectrum lines representing individual
elements provide a rough idea of the relative concentrations of those elements in the
alloy. Precise measurement of element concentrations requires more complicated
quantitative analysis, which will be introduced in Section 6.4.
While WDS provides high resolution and high ratio of signal to background,
analysis of the spectra can be complicated. Equation (6.2) (Bragg’s Law) indicates
that the orders of diffraction (n) may generate multiple wavelength peaks in a
spectrum for the same characteristic line. For example, given a specific characteristic
X-ray line with the wavelength (λ) emitted from a specimen, there may be three
peaks corresponding to n = 1, 2, and 3. In addition, if a specific wavelength is
nearly equal to a multiple of another wavelength, then their peaks will appear
201
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6.2 X-Ray Fluorescence Spectrometry
6 X-Ray Spectroscopy for Elemental Analysis
(a)
Energy (keV)
4.96
5.51
6.2
7.08
8.26
Indensity
Ni Kα
V Kα1.2
Ni Kα
Cr Kα1.2
Co Kα
Ni Lα
V Kβ
Co Kβ
Cr Kβ
2.25
2.50
4.96
1.75
W Lα
1.5
6.0
Wavelength (Å)
Energy (keV)
(b)
1.30 1.38 1.46 1.55 1.65 1.71 1.91
Indensity
Al Kα
Ta Mα
W Mα
Re Mα
Al Kβ
9.5
9.0
8.5
8.0
7.5
7.0
6.5
Wavelength (Å)
Figure 6.8 WDS spectra of a nickel-based superalloy: (a) spectrum obtained with a LiF
analyzing crystal and (b) spectrum obtained with a TAP crystal. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1].© 1992 Springer Science.)
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202
superimposed on each other in the spectrum. For example, SKα (n = 1) has a
wavelength of 5.372 Å, which is very close to three times the CoKα wavelength
(1.789 Å × 3 = 5.367 Å). Thus, the SKα line will likely be superimposed on the third
order (n = 3) CoKα line. We should be aware of all of these special problems in
interpreting a WDS spectrum.
6.2.2
Energy Dispersive Spectroscopy
EDS became a commercial product in the early 1970s, and rapidly overtook WDS in
popularity. An EDS system is structurally simple because it does not have moving
parts such as the rotation detector with WDS. EDS systems are relatively faster
because the detector collects the signals of characteristic X-rays energies from a
whole range of elements in a specimen at the same time rather than collecting
signals from X-ray wavelength individually. For EDS, the typical resolution of
energy dispersion is about 150–200 eV, worse than the corresponding resolution
of WDS, and the lightest element that can be detected is O (Z = 8), not C (Z = 6).
But these disadvantages are not as important as the advantages of an EDS system,
which are low cost and fast analysis.
6.2.2.1 Detector
The Si(Li) is the most commonly used detector in an EDS system. The Si(Li)
detector consists of a small cylinder of p-type silicon and lithium in the form of a
Si(Li) diode, as schematically shown in Figure 6.9. X-ray photons collected by the
X-ray Photon
a
b
c
a
Figure 6.9 A Si(Li) cylinder with annular groove construction: (a) p-type silicon; (b) lithium
compensated region; and (c) n-type silicon.
203
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6.2 X-Ray Fluorescence Spectrometry
6 X-Ray Spectroscopy for Elemental Analysis
detector generate a specific number of electron–hole pairs. The average energy of
photons needed to generate as electron–hole pair (ei ) is about 3.8 eV in the Si(Li)
diode. The higher the photon energy, the more pairs are generated. Characteristic
X-ray photons can be separated by their energy levels according to the numbers of
electron–hole pairs they generate.
The electron–hole pairs, as the electric charge, are swept from the detector diode.
A preamplifier collects the charge to produce an output of electrical pulse whose
voltage amplitude is proportional to the X-ray photon energy. The energy resolution
of the detector (R) in eV can be estimated
2
R = σnoise
+ [2.35(ei FE)]2
(6.4)
E is the energy of characteristic X-ray line and F is a constant called the Fano
factor, which has a value of 0.12 for Si(Li). σ noise , the electronic noise factor, plays
an important role in the resolution. Reduction of the electronic noise will improve
the resolution of the EDS detector. Thus, the Si(Li) diode and the preamplifier
are mounted in a cylindrical column (the cryostat) so that they can operate at the
temperature of liquid nitrogen (−196 ◦ C) in order to reduce the electrical noise and
increase the signal-to-noise ratio.
X-ray photons must pass through a window to reach the Si(Li) diode. This window
is typically made of a light element, beryllium. Beryllium, like any material, will
absorb X-ray photons, even though its absorption is weak. Thus, the sensitivity of
the detector will be affected by the beryllium window. In order to reduce the photon
absorption, the beryllium has to be as thin as possible, especially for detecting light
elements of which the characteristic energies are on the order of 100 eV. The typical
thickness of the beryllium window is about 10 μm.
6.2.2.2 Energy Dispersive Spectra
An EDS spectrum is presented as the intensity of characteristic X-ray lines across
the X-ray energy range. A spectrum in a range from 0.1 to about 10–20 keV
can show both light and heavy elements because both K lines of light elements
and M or L lines of heavy elements can be shown in this range. For example,
Figure 6.10 shows the EDS spectrum of a glass specimen containing multiple
elements including Si, O, Ca, Fe, Al, and Ba in an energy range up to 10 keV.
EDS spectra are similar to WDS spectra, but identification of individual elements
from EDS spectra is more straightforward than from WDS spectra because each
characteristic line generated by a specific element exhibits a unique X-ray energy.
However, the signal-to-noise ratio is lower than that of WDS, and the resolution,
in terms of energy, is about 10 times lower than that of WDS. Even so, EDS is an
attractive technique for qualitative analysis of elements.
6.2.2.3 Advances in Energy Dispersive Spectroscopy
All the early EDS systems were operated in a primary mode in which X-rays emitted
from the X-ray tube irradiate the specimen directly. This had drawbacks because the
X-rays could excite more photons than could be counted by the detector, because
there is a maximum counting rate of photons for an energy detector. If the number
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204
3022
Si Kα
Al Kα
O Kα
Fe Lα
Ca Kα
Ba Lα
Fe Kα
Ca Kβ
Ba Lβ1
Fe Kβ
Ba Lβ
0
0.01
10.00
keV
Figure 6.10 EDS spectrum of glass which includes Si, O, Ca, Al, Fe, and Ba. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1] .© 1992
Springer Science.)
of characteristic photons excited in the specimen is too great, a portion of photons
may not be counted. Thus, the measured intensities may be lower than the actual
emitted intensity of X-ray photons. The period during which the detector cannot
respond to the number of photons correctly is called the dead time of the detector.
The dead time is in the order of 0.5 × 10−7 s.
Later, a secondary mode of EDS was developed to overcome this intrinsic
limitation of the detector when handling a large influx of photons. In the secondary
mode, a selected pure element standard with absorption filters is placed in the
optical path between the primary X-ray source and the specimen. The element
standard only allows the X-ray photons in a selected range of energy (secondary
photons) to strike the sample. Thus, in secondary photon radiation, the number
of photons emitted from the sample is controlled by preventing unwanted X-ray
excitation of the specimen.
Another problem of early EDS systems was the difficulty in examining small
samples, of which the signals of characteristic X-rays are weak compared with
background noise in a spectrum. This problem can be solved by use of the total
reflection X-ray fluorescence spectrometer (TRXRF). The TRXRF technique is based
on the phenomenon that the reflectivity of a flat target strongly increases below a
critical glancing angle. This instrumentation is illustrated in Figure 6.11. The Si(Li)
detector is placed close to (∼5 mm) and directly above the specimen. The primary
X-ray radiation enters the specimen at a glancing angle of less than 0.1◦ , rather
than at 40◦ as in a conventional EDS. The sample is presented as a thin film on
the optically flat quartz plate. Reflectors and apertures between the X-ray tube and
sample ensure that the angle at which radiation enters the sample is slightly less
205
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6.2 X-Ray Fluorescence Spectrometry
6 X-Ray Spectroscopy for Elemental Analysis
Energy dispersive
detector
X-ray tube
Fluorescence
rediation
Sample on
optical flat
Totally reflected
beam
Figure 6.11 Geometric construction of a total-reflection fluorescence spectrometer. The incident angle is less than 0.1◦ so that the primary X-ray beam is totally reflected from the
flat substrate. (Reproduced with permission from Ref. [3].© 1997 John Wiley & Sons Inc.)
than the critical angle of total reflection. The critical angle refers to an incident angle
below which no penetration of radiation into the quartz substrate occurs. TRXRF
eliminates primary X-rays radiating from substrate materials to a large extent.
Thus, the X-ray signals in the EDS spectrum from sources other than the sample
can be significantly reduced. This technique enables us to measure elements from
solid samples with low mass down to 10−12 g.
6.2.3
XRF Working Atmosphere and Sample Preparation
An XRF spectrometer can work in an internal atmosphere of air, helium, or
vacuum. However, detection sensitivity of fluorescent X-rays is highly affected
by the atmosphere. A vacuum atmosphere provides the best sensitivity. Helium
is better than an air atmosphere. The sensitivity differences for light elements
detection are quite striking. For example, an EDS-type spectrometer can detect
elements down to carbon (atomic number 6) in vacuum, but limits its detection
to sodium (atomic number 11) in helium, and to aluminum (atomic number 13)
in air. Thus, most XRF systems work in a vacuum atmosphere with options of
working in helium and air.
Material samples for examination in an XRF spectrometer can be bulk, powder,
and liquid. The basic requirements for solid samples are chemical homogeneity
and physical flatness of the face pointing towards the primary X-ray irradiation.
The samples are commonly contained in cup-type sample holders with a diameter
of 25–48 mm. A bulk sample larger than that can also be examined in XRF with
a special holder. The largest sample can be of a size of over 400 × 300 × 100 mm.
The primary X-ray irradiates an area of sample (∼5 cm2 ) from the bottom of the
sample holder. We should note that X-ray penetration into a solid is limited to tens
of micrometers from a solid surface even though the thickness of a solid sample
can be tens of millimeters. Thus, the sample should be chemically homogeneous
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206
so that composition of a thin layer near the surface is the same as the whole sample;
otherwise its XRF spectrum does not represent its true chemical composition. On
the other hand, a sample should have sufficient fine surface finishing. A rough
sample surface might cause intensity loss of the fluorescent X-ray in a spectrum,
because the rough surface features might increase the path length from where the
characteristic X-rays are emitted in a sample to the sample surface. Commonly, the
surface roughness for a short wavelength X-ray emission should be of 100 μm or
less, and for a long-wavelength one should be limited to 10–50 μm.
A bulk solid sample with a homogeneous composition can be directly examined
in a XRF spectrometer after surface polishing. The polishing process introduced
in Chapter 1 is suitable for XRF sample preparation. However, the process
should avoid any chemical contamination of the sample surface. A bulk solid with
heterogeneous composition should go through special treatment. The treatment
methods include dissolution, chemical reaction, and melting in order to reach
chemical homogeneity.
A powder sample is commonly ground and then pressed into pellets with high
pressure. The grinding process is to ensure fineness of powder particle size even if
the powder is chemically homogeneous. We should note that a powder is subjected
to chemical contamination by grinding devices, which should be carefully avoided.
Small amounts of powder samples, which cannot make a pellet, can be stuck to a
sample held with organic binder, such as paraffin. A heterogeneous powder sample
needs to be treated and the most effective method is the borax fusion. The method
is to dissolve powder at high temperature with an excess of sodium or lithium
tetraborate and casting into a glassy pellet.
A liquid solution sample can be directly examined in a special liquid sample
holder with an X-ray transparent bottom. The bottom is commonly made of Mylar
(polyester film) and polypropylene film. A helium atmosphere is often required
to reduce fluorescent X-ray attenuation when examining liquid samples. The low
concentrations of elements in liquids may require a preconcentration treatment.
The treatment includes evaporation, surface adsorption on activated carbon, and
use of an ion-exchange resin. An ion-exchange resin collects certain elements from
a liquid and then a filter paper collects the resin for XRF examination.
6.3
Energy Dispersive Spectroscopy in Electron Microscopes
The EDS type of X-ray spectrometer is commonly included as a part of scanning
electron microscopes (SEMs) and TEMs. The reason for using EDS rather than WDS
is simply its compactness. With EDS in an EM, we can obtain elemental analysis
while examining the microstructure of materials. The main difference between
EDS in an EM and in a standalone XRF is the source to excite characteristic X-rays
from a specimen. Instead of using the primary X-ray beam, a high-energy electron
beam (the same beam for image formation) is used by the X-ray spectrometer in
the microscopes. EDS in an EM is suitable for analyzing the chemical elements in
207
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6.3 Energy Dispersive Spectroscopy in Electron Microscopes
6 X-Ray Spectroscopy for Elemental Analysis
microscopic volume in the specimen because the electron probe can be focused on
a very small area. Thus, the technique is often referred to as microanalysis.
6.3.1
Special Features
The structure of EDS in an EM is illustrated as in Figure 6.12, using an SEM
system as an example. EDS in the SEM is fundamentally similar to a standalone
EDS except for the primary beam source. In the SEM, the electron beam aligns
with the vertical axis of the microscope so that the Si(Li) detector has to be placed
at a certain angle from the vertical. The angle between the surface plane of the
specimen and detector is called the take-off angle and is often referred to as the
angular position of the detector. The take-off angle can be changed by rotating
the specimen surface with respect to the detector. For a low take-off angle, a rough
surface may interfere with collection of X-ray photons emitted from a valley area,
as illustrated in Figure 6.13. Such problems do not occur if the specimen has a
microscopically flat surface.
Dete
c
com tor
llima
tor
Polepiece
Spec
Stage
Figure 6.12 Geometrical arrangement of EDS in a scanning electron microscope (SEM).
(Reproduced with kind permission of Springer Science and Business Media from Ref. [1].©
1992 Springer Science.)
Electron beam
X-ray detector
Sample surface
Take-off angle
Figure 6.13
Potential interference of X-ray detection due to low take-off angle in the SEM.
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208
Although the ability to focus the electrons as a probe enables us to analyze
chemical elements in a microscopic area, we should realize that the minimum
specimen area that EDS can resolve is not equal to the diameter of the electron
probe. The characteristic X-rays are excited from a volume under the surface of the
specimen, not from an area on the surface. As shown in Figure 6.14, the volume is
pear-shaped and its lateral size can be significantly larger than the size of the probe.
It is important for us to know, when analyzing a microscopic area of a bulk specimen in an SEM, that EDS signals are emitted from a lateral area that is much larger
Eo
(a)
Eo
20 keV
dp
dp
R
R
Ec
Ec
AI K
Cu K
Ec
E=O
Cu L (AI K)
(b)
6
RAI
ρ = 2.7 g/cc
Range R(X), μm
5
Cukα in AI
4
AIKα in AI
3
CuLα in Cu
2
CuKα in Cu
1
AuLα in Au
0
0
5
10
15
20
25
30
35
Eo (keV)
Figure 6.14 (a) Comparison of X-ray production regions with specimens of different
mass densities (ρ = 3 and 10 g cm−3 for
left and right examples, respectively) and
(b) spatial resolution of EDS as a function of acceleration voltage of electrons and
specific lines of characteristic X-rays emitted
from bulk specimens. (Reproduced with kind
permission of Springer Science and Business Media from Ref. [1].© 1992 Springer
Science.)
209
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6.3 Energy Dispersive Spectroscopy in Electron Microscopes
6 X-Ray Spectroscopy for Elemental Analysis
than the probe diameter. Thus, the spatial resolution of EDS should be considered
when we are interested in elemental analysis of a microscopic feature in the SEM.
The volume emitting X-rays (emission volume) is that in which primary electron
energy is still greater than the energy required to excite the specific line of
characteristic X-rays (E ex ). The emission volume is determined by the acceleration
voltage of electrons (E o ) and the characteristics of the specimen’s component
elements, such as mass density (ρ) and E ex . The emission volume has been
estimated with the depth of characteristic X-ray generation (R).
R=
1.7
)
0.064(Eo1.7 − Eex
ρ
(6.5)
It is reasonable to assume the lateral size of the emission volume is about the same
as the depth of the emission volume. Thus, R can represent the spatial resolution of
EDS microanalysis. Figure 6.14a illustrates the depth of X-ray generation (R) with
the same electron beam energy in two microscopic areas with different densities.
Figure 6.14b shows that the resolution will be improved by reducing the acceleration
voltage of electron beam (E o ) for characteristic lines of different elements. To obtain
a better spatial resolution, we should choose an acceleration voltage that is not
much higher than that necessary to excite characteristic X-rays in the specimen.
For thin specimens, as used in a TEM, the spatial resolution is of less concern.
The lateral size of the emission volume is not significantly larger than the probe
size because the thinness of the specimen limits the spread of the emission volume.
For example, with a TEM acceleration voltage of 100 kV and probe diameter of
20 nm, the lateral size will be about 23 nm for aluminum. The electron beam size
can be reduced to about 0.5 nm in advanced TEM systems. Thus, chemical analysis
of nanometer-sized particles can be achieved in TEM systems.
6.3.2
Scanning Modes
EDS offers two modes of examination: stationary and scanning. In the stationary
mode, the probe stays at one location until the collection of X-ray photons is
complete. The dwell time of the probe for EDS analysis is determined by the
number of X-ray photon counts received by the detector. Elemental detection relies
on the signal-to-noise ratio. As discussed in Chapter 4, the longer the dwell time,
the higher the counts of characteristic X-ray photons. Low concentration of trace
elements (< 1 wt%) requires longer dwell times for their detection.
In the scanning mode, the electron probe moves over the specimen surface,
similar to the way in which the probe moves for obtaining an electron image
in the SEM. The intensity of specific characteristic X-rays can be recorded and
superimposed on the corresponding electron image as shown in Figure 6.15. The
line scans of elements help us to identify the element distribution shown in the SEM
image. Also, we can use the scanning mode to make composition maps in which the
distributions of elements are clearly revealed. Figure 6.16 shows element maps of
an alloy sample in which distributions of alloy elements are revealed by gray scales.
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210
Figure 6.15 Co and Cr line scans across an oxidized high-temperature alloy. The top curve
is for cobalt and the bottom curve is for chromium. (Reproduced with kind permission of
Springer Science and Business Media from Ref. [1].© 1992 Springer Science.)
We may select the stationary mode to analyze the elements in microscopic
features such as impurities, precipitates, and grain boundaries. We may select the
scanning mode to examine the composition change in a certain dimension of the
specimen or composition variations in a selected area of a specimen.
6.4
Qualitative and Quantitative Analysis
6.4.1
Qualitative Analysis
Identifying the chemical elements in specimens by X-ray spectrometers is in many
ways similar to identifying chemical compounds by X-ray diffractometry (XRD).
However, identifying elements is relatively easy because there are only about 100
elements, while there are several million chemical compounds. We may only find
a major peak with a few minor peaks of a certain element in WDS and EDS,
not several tens of peaks for a crystalline compound as in an XRD spectrum. For
example, Figure 6.17 shows an XRF spectrum (EDS type) for a Ni–Ti alloy. The
spectrum shows one major Kα peak and one minor Kβ peak for each of Ni and
Ti. The Kα includes Kα 1 and Kα 2 , which are often overlapped in the spectrum due
to the small difference in their energy levels. The relative positions and intensities
of the α and β lines also can help us to identify chemical elements if there is a
possibility that the Kα or Kβ line of one element overlaps another element’s L lines.
We should note that the primary X-ray source of XRF includes both continuous
and characteristic radiation. The continuous X-rays generate the background of
211
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6.4 Qualitative and Quantitative Analysis
6 X-Ray Spectroscopy for Elemental Analysis
100 μm
100 μm
(a)
(b)
100 μm
100 μm
(c)
(d)
Figure 6.16 EDS maps of a polished area of an alloy specimen. The distributions and concentrations of chemical elements shown in the maps include: (a) Si; (b) Mo; (c) Cr; and
(d) Co. (Reproduced with permission from Ref. [4]. © 1988 Taylor & Francis Group Ltd.)
45.0
Ti (Kα)
40.0
35.0
Counts (×103)
30.0
Ni (Kα)
25.0
20.0
15.0
10.0
Ti (Kβ)
5.0
0.0
0.00
Figure 6.17
1.50
3.00
4.50
6.00
keV
Ni (Kβ)
7.50
9.00 10.50 12.00
EDS spectrum of a Ni–Ti alloy obtained in an XRF spectrometer.
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212
the spectrum. The primary characteristic X-rays will generate additional peaks in a
spectrum. Thus, such background and additional peaks of a target material of the
X-ray tube should be deducted from a spectrum. For XRF, an uncommon element
such as rhodium (Rh) is often selected as the target material of X-ray tube in order
to reduce confusion in identifying elements in samples. For example, Figure 6.18
shows the EDS spectrum of a lead alloy in which the Rh peaks are not overlapped
with peaks of sample elements.
Modern X-ray spectrometers are equipped with computer software that is fully
capable of identifying the possible elements from a spectrum. We can input the elements that possibly exist in the specimen into the software for qualitative analysis.
The computer software will mark peak positions of the input elements in the spectrum. Also, the software will generate such peak lines with correct relative intensities
in a spectrum, for example, a correct intensity ratio of Kα to Kβ. With computer
assistance, the errors in element identification can be reduced to a minimum.
6.4.2
Quantitative Analysis
We often want to know not only the identity of chemical elements but also
their concentrations in a specimen. Thus, quantitative elemental analysis is often
required. The concentrations of elements must relate to their peak intensities in the
spectrum, similar to the relationship between weight fractions of crystalline phases
and their peak intensities in the XRD spectrum. Chemical compositions should be
56.0
48.0
Counts (×103)
40.0
Pb
32.0
Pb
24.0
8.0
Rh
Zr Rh
Rh
Ti
Rh Sb
Pb Pb
Sb Ti
0.0
0.00
2.00
16.0
4.00
Pb
6.00
Pb
Pb Pb
Zr
Pb
Pb
Zr
Zr
8.00 10.00 12.00 14.00 16.00 18.00 20.00
keV
Figure 6.18 XRF spectrum of a Pb alloy with primary X-ray radiation from the X-ray tube
with a Rh target. The Rh characteristic lines are not overlapped with those of elements in
the alloy specimen.
213
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6.4 Qualitative and Quantitative Analysis
6 X-Ray Spectroscopy for Elemental Analysis
calculated by comparing the ratios of integrated peak intensities among elements
in the specimen. In general, the weight fraction (C) of an element in relation to the
relative intensities of its peaks (IR ) is mainly affected by the instrument factor (K),
and the matrix factor of specimen (M).
C = M × K × IR
(6.6)
The instrument factor K includes conditions of primary sources, the geometrical
arrangement of a specimen with respect to the radiation and detection, and detector
characteristics. The matrix factor refers to the interactions among the elements in
the specimen.
There are three main matrix effects in XRF: primary absorption, secondary absorption, and secondary fluorescence. Primary absorption refers to the radiation that is
absorbed on the beam’s path to reach the atoms to be excited. Secondary absorption
refers to absorption of fluorescent radiation from atoms that occur along its path
inside the specimen to the detector. Secondary fluorescence refers to the fluorescent
radiation from the atoms that are excited by the fluorescent radiation of atoms with
a higher atomic number in the same specimen. This phenomenon is possible when
the energy of the primary fluorescent radiation from heavier atoms is sufficient
to excite secondary fluorescence from lighter atoms in the specimen. The absorption effects reduce the intensity of characteristic X-ray lines in spectrum, while
secondary fluorescence increases the intensity of lighter elements. The matrix
factors of EDS analysis in an EM are described in a later section of this chapter.
Specimen-preparation conditions may also affect the relation between intensity and
concentration, such as chemical homogeneity. For accurate quantitative analysis,
either a standard sample of pure elements to be analyzed or a sample with similar
composition to that of the specimen is needed to determine factors M and K in
Eq. (6.6) precisely.
The following sections will briefly introduce the methods of quantitative analysis
by XRF and EDS in EM, separately. There are differences in the factors affecting
the analysis because EDS in EM uses an electron beam rather than X-rays as the
primary source.
6.4.2.1
Quantitative Analysis by X-Ray Fluorescence
Internal Standard Method There are several methods of quantitative analysis in
XRF. For analyzing a single element in a specimen, we may use an internal standard
method, one of the most useful techniques for determining a single element weight
fraction in a known or unknown matrix. The internal standard refers to adding a
standard element of a known concentration into the specimen. Adding a standard
element into the specimen is possible if the specimen is a powder or a liquid type.
This method is based on the assumption that the instrumental and matrix effects
are the same for the standard and the element to be analyzed. Thus, we can obtain
the weight fraction of element (Cx ) from its measured X-ray intensity (Ix ) with
knowledge of the weight fraction of standard element (Cs ) and its corresponding
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214
intensity (Is ) by the following relationship.
Cx
I
= x
Cs
Is
(6.7)
The instrument factor for the standard and the element to be analyzed should
be the same when their intensities are obtained under identical instrumental
conditions. However, the matrix factor of the standard element and the element
to be analyzed could be different. The differences may arise from differences in
the chemical element or concentrations. To reduce the difference in the matrix
factor, the standard element should have an atomic number close to the element
to be analyzed and should have the same concentration level as the element to
be analyzed. Also, the internal standard method should be used for analyzing an
element with low concentration (< 10%) to avoid excessive amounts of the standard
element being added to the specimen. A significant amount of the standard element
would change the characteristics of the matrix. In addition, good mixing of the
standard elements with the specimen and similar particle size between the standard
and specimen are necessary.
6.4.2.2 Fundamental Parameter Method
For a modern XRF equipped with a powerful computer system, the fundamental
parameter method (FP method) is most widely used for quantitative analysis.
The method determines the concentration of an element when its theoretical
intensity matches its measured intensity. The fluorescence X-ray intensity of
a given composition can be calculated using theoretical formulas with given
specimen physical and instrumental parameters. The physical parameters include
specimen density, thickness, X-ray absorption coefficients, and fluorescence yield.
The instrumental parameters include excitation voltage of the X-ray tube, optical
geometry, and detector characteristics.
During quantitative analysis, the computer estimates the composition of the
specimen from a measured intensity spectrum. Then, its theoretical intensity
is calculated using the FP method. The theoretical intensity, which is on a
relative scale, should be converted to the same scale as the measured intensity
by multiplying with an instrumental sensitivity. The intensity difference between
the measured intensity and calculated intensity will trigger a new estimation of
composition and start a new cycle of calculation. The final composition is obtained
when the difference between the calculated intensity and measured intensity is
less than a threshold level. This instrumental sensitivity for each element should
be obtained by either measuring the intensity of a standard sample containing
the known elemental concentration under the same instrumental conditions or
by consulting a sensitivity database stored in the computer. The FP method
requires extensive calculation, which is only practical since personal computers
have become so powerful. The great advantage of the FP method is that it can
analyze the specimen when relevant standard samples are not available. This
feature is extremely useful in many research situations.
215
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6.4 Qualitative and Quantitative Analysis
6 X-Ray Spectroscopy for Elemental Analysis
6.4.2.3 Quantitative Analysis in Electron Microscopy
In general, quantitative analysis by EDS in EM is similar to that of XRF. The
analytical methods, however, are different for two main reasons. First, the interactions between the electron beam and specimen are different from those of
primary X-ray radiation. Secondly, an EM specimen for chemical analysis cannot be
modified as in the internal standard method. For accurate quantitative analysis of
EDS in EMs, separate standard samples containing the elements in the specimen
to be analyzed are necessary. The standards should be measured under identical
instrumental conditions to the specimen. This means that the spectra of specimen
and standard should be collected under the same conditions with regard to the
following parameters:
• acceleration voltage of the electron beam;
• X-ray take-off angle from specimen to detector; and
• detector coincidence loss (detector dead time).
Even so, the differences in matrix effects between the specimen and standard
cannot be ignored. The general formula of quantitative analysis with a standard is
expressed by an equation that includes matrix effects
Ci
I
= (Zi Ai Fi ) i = (Zi Ai Fi )ki
C(i)
I(i)
(6.8)
The expression (Zi Ai Fi ) represents the matrix factors affecting the X-ray intensity
of element i in the specimen (Ii ) and in standard (I(i) ), which can be divided
into three major types: atomic number effect (Zi ), X-ray absorption (Ai ), and X-ray
fluorescence (Fi ). Equation 6.8 represents the quantitative method, called the ZAF
method. It is the most commonly used technique that determines composition by
calculating the (Zi Ai Fi ) for each element in the specimen. The ZAF method
is suitable for quantitative analysis of heavy and medium-weight elements. To
understand the method, we need to know about Z, A, and F factors.
The atomic number factor (Z) counts the difference in characteristic X-rays
generation due to atomic number change in the matrix. It arises from two
phenomena: electron backscattering (R) and electron retardation (S). A fraction of
primary electrons (R < 1) is backscattered and does not generate X-rays. Recalling
Chapter 4, backscattering effects are a function of atomic number. An element in
a matrix with elements heavier than it will generate a lower intensity than it does
in pure form. Electron retardation represents the continuous electron energy loss
that occurs when electrons travel in a specimen due to inelastic scattering. This
effect is expressed as the stopping factor (S)
S=
1 dEo
ρ ds
(6.9)
S is a function of electron travel distance in the specimen (s), acceleration voltage
of electrons (E o ), and specimen density (ρ). S decreases while R increases with
increase in atomic number.
The X-ray absorption factor (A) counts the decrease in density of characteristic
X-rays from emitting location to detector. The absorption follows an exponential
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216
relationship as shown in Eq. 2.2.
Ix = Io exp[(μ/ρ)ρt]
(6.10)
The absorption is strongly affected by the absorption coefficient (μ), density (ρ),
and path length (t) that X-rays travel within a specimen before reaching its surface.
The X-ray absorption is the greatest factor affecting X-ray intensity. For a certain
path length, the X-ray intensity is significantly affected by the mass absorption
coefficient (μ/ρ). For example, the μ/ρ difference between Fe and Al in a Ni matrix
is more than a factor of 5, comparing 90 with 4837 cm2 g−1 .
The fluorescence factor (F) arises from the excitation of characteristic X-rays of
the element to be analyzed by the characteristic X-rays emitted from matrix atoms.
This phenomenon occurs when the characteristic X-rays from matrix elements
have energies greater than that required for exciting characteristic X-rays of the
element to be analyzed. Thus, the resulting X-ray intensities of the element to
be analyzed will be enhanced by the fluorescence effect. The fluorescence factor
is usually less important than the matrix factor, because fluorescence X-rays may
not exist, or the concentration of elements emitting fluorescence X-rays may
be small.
The ZAF method relies extensively on a computer, similar to the FP method. First,
the weight fraction of elements in the specimen is estimated from their relative
intensities (ki / i ki ). Then, the (Zi Ai Fi ) factor for each element is estimated and
is used for calculating ki . The calculated ki will compare with the measured ki . The
iteration of computation continues until the two values converge.
The possible errors for ZAF correction in the analysis will be amplified for
light elements (Z < 10), because in theoretical calculations of (Zi Ai Fi ) factors,
approximations that are valid for medium-weight and heavy elements fail to apply
for light elements. Thus, other methods specially designed for light elements are
needed.
The ZAF method is based on assumptions that the specimen is in bulk and its
surface is microscopically flat. Thus, we should be cautious when a specimen does
not meet these assumptions, such as a thin-film specimen or a specimen with a
rough surface. For example, with a thin-film specimen, the matrix effect will be
reduced and the intensity–weight fraction relationship will be simplified.
Standardless quantitative analysis is often available in the EDS system of an EM.
The standardless technique is desirable when standards are not available. The
standardless technique is based on prediction of the X-ray intensity that would be
obtained from a pure element standard under the same instrumental conditions.
This method works well for a specimen consisting of transition elements of
which the K lines span the range 5–10 keV, such as stainless steel. The method
should be used cautiously because it potentially generates large errors that we may
not recognize. Standardless analysis may generate large errors for specimens in
which the elements generate low-energy lines (< 3 keV). The standardless method
may generate considerable errors when multiple X-ray families, K, L, and M, are
involved in the analysis. There are several ways we can double-check the result
217
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6.4 Qualitative and Quantitative Analysis
6 X-Ray Spectroscopy for Elemental Analysis
of standardless analysis; for example, we can use a different family of X-ray lines
(K and M), change electron beam energy, or change the count rate.
Questions
6.1 In a characteristic X-ray spectrum, Kα and Kβ lines should always appear
in pairs. What are the characteristics of the Kβ line, compared with the Kα
line, in a spectrum?
6.2 Compare the similarities of, and differences between, X-ray diffractometry
and X-ray fluorescence spectrometry.
6.3 For an industrial application that requires fast identification of elements,
which XRF system (WDS or EDS) would you choose? What are the benefits
and disadvantages of your choice?
6.4 Count the total number of K lines for electron transitions from L and M
shells to the K shell.
6.5 How would you adjust the X-ray tube to ensure the excitation of fluorescence
X-rays with energy of 15 keV? Why should we choose appropriate target
materials in the X-ray tube for XRF?
6.6 Select analyzing crystals of WDS to detect the K lines of elements Ca, Si, Na,
and N.
6.7 Is the synthetic microstructure (LSM) in WDS able to detect B and Be? Why
do people commonly believe C is the lightest element that can be detected
by WDS?
6.8 Commonly, an EDS spectrum is recorded in the range 0–20 keV. What are
the possible K, L, and M lines to be detected in a specimen containing Mg,
Zn, Ag, and Au?
6.9 Estimate the maximum energy resolution of EDS with the Si(Li) detector for
O, Ca, Cu, and Au.
6.10 Why should the Si(Li) detector of an EDS instrument be cooled by liquid
nitrogen? Why may we detect light elements such as C and O without a
beryllium window on the EDS detector?
6.11 Why are we likely to overestimate the weight fraction of Ni from the WDS
spectrum of a specimen containing Ni and Ag? Is there any way to detect
this error by examining the spectrum?
6.12 Determining the Ca/P ratio in calcium phosphate is important for its phase
identification. Often the Ca/P ratio is undervalued by the standardless
quantitative analysis of EDS in SEM. Can you speculate on the reasons?
6.13 Samples to be examined by XRF can be either in solid, powder, or thin film
type. Often, it is required that the thickness of a thin-film sample should be
less than 10 μm in quantitative analysis. Why?
6.14 What change in the EDS spectrum do you expect when a specimen is tilted
to face the detector in an SEM?
6.15 Can you use the ZAF method for quantitative analysis for EDS in a TEM?
Why or why not?
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218
References
Further Reading
1. Goldstein, J.I., Romig, A.D. Jr.,
Brandon, D. and Kaplan, W.D. (1999)
Microstructural Characterization of Materials, John Wiley & Sons, Ltd, Chichester.
Jenkins, R. and Snyder, R.L. (1996) Introduction to X-Ray Powder Diffractometry, John
Wiley & Sons, Inc., New York.
Lifshin, E. (1999) X-Ray Characterization
of Materials, Wiley-VCH Verlag GmbH,
Weinheim.
Jenkins, R., Gould, R.W., and Gedcke, D.
(1995) Quantitative X-Ray Spectrometry,
2nd edn, Marcel Dekker, New York.
Goldstein, J.I. and Yakowitz, H. (1977) Practical Scanning Electron Microscopy, Plenum
Press, New York.
Newbury, D.E., Lyman, C.E., Echlin, P.,
Fiori, C., Joy, D.C., and Lifshin, E. (1992)
Scanning Electron Microscopy and X-Ray
Microanalysis, 2nd edn, Plenum Press,
New York.
2. Jenkins, R. (1999) X-Ray Fluorescence
Spectrometry, 2nd edn, John Wiley &
Sons, Inc., New York.
3. Klockenk mper, R. (1997) TotalReflection X-ray Fluorescence Analysis, John Wiley & Sons, Inc.,
New York.
4. Goodhew, P.J. and Humphreys,
F.J. (1988) Electron Microscopy and
Analysis, 2nd edn, Taylor & Francis,
London.
219
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Further Reading
7
Electron Spectroscopy for Surface Analysis
Electron spectroscopy is a technique that uses characteristic electrons emitted
from a solid for elemental analysis, not for microstructure imaging as in electron
microscopy. The characteristic electrons (either Auger electrons or photoelectrons)
exhibit characteristic energy levels, revealing the nature of chemical elements in
the specimens being examined. Auger or photoelectrons can only escape from
the uppermost atomic layers of solid (a depth of 10 nm or less) because their
energies are relative low (generally 20–2000 eV), while the characteristic X-rays
can escape from a much greater depth (several micrometers from the surface).
Thus, electron spectroscopy is a technique for surface chemical analysis. There are
two types of electron spectroscopy: Auger electron spectroscopy (AES) and X-ray
photoelectron spectroscopy (XPS). Auger electrons and photoelectrons are different
in their physical origins, but both types of electrons carry similar information about
chemical elements in material surfaces.
7.1
Basic Principles
7.1.1
X-Ray Photoelectron Spectroscopy
The X-ray photoelectron is an electron ejected from an electron shell of an atom
when the atom absorbs an X-ray photon. Figure 7.1a schematically illustrates the
emission of a photoelectron from an atom when it is excited by an X-ray photon.
As mentioned in Chapter 6, an incident X-ray photon can have sufficient energy
(a value of hv) to knock out an inner-shell electron, for example, from the atom’s
K shell. In such a case, the K-shell electron would be ejected from the surface as
a photoelectron with kinetic energy EK . Knowing the kinetic energy EK , we can
calculate the binding energy of the atom’s photoelectron (E B ) based on the following
relationship
EB = hv − EK − Φ
(7.1)
is the parameter representing the energy required for an electron to escape from
a material’s surface, h is Planck’s constant and ν is the frequency. The value of Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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221
7 Electron Spectroscopy for Surface Analysis
Photoelectron
e−
Auger
electron
e−
e−
hv
or
L2,3
L2,3
L1
L1
hv
e−
K
K
(a)
XPS
(b)
Auger
Figure 7.1 Emission processes of characteristic electrons: (a) a 1s photoelectron and (b) a
KL1 L2,3, Auger electron.
depends on both the sample material and the spectrometer. The binding energies
of atomic electrons have characteristic values, and these values are used to identify
elements, similar to the way that the characteristic X-ray energy is used in X-ray
spectroscopy. XPS identifies chemical elements from the binding energy spectra of
X-ray photoelectrons. A typical XPS spectrum is a plot of intensity versus binding
energy. Photoelectrons are ejected from different electronic shells and subshells.
Each binding energy peak is marked as an element symbol plus a shell symbol from
where the photoelectron was emitted, for example, Al 2p, O 1s, and so on, as shown
in Figure 7.2. The photoelectrons emitted by subshells p, d, and f are commonly
marked with an additional fraction number; for example, Cu2p 1 . There are 12 and
2
3
for the p subshell, 32 and 52 for the d subshell, and 52 and 72 for the f subshell.
2
These fractions represent the quantum number of total angular momentum (J)
for an individual shell electron, as mentioned in Section 6.1.1. An XPS spectrum
may also contain peaks from Auger electrons. For example, the spectrum shown
in Figure 7.2 includes Auger electron peaks marked as O KLL and C KLL. The
generation of Auger electrons is discussed in the following section.
7.1.2
Auger Electron Spectroscopy
Auger electrons were named after Pierre Auger who, together with Lise Meitner,
discovered Auger electron emission in 1920s. The Auger electrons were mentioned
in the discussion of the interaction between incident electrons and atoms in
Chapter 6. Figure 7.1b illustrates the emission process of an Auger electron. When
a high-energy electron (or X-ray photon) strikes an inner-shell electron of an atom,
the energy of the incident particle can be high enough to knock out the inner-shell
(K shell in Figure 7.1b) electron. Thus, the atom becomes ionized and in an
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222
223
OIs
90
Kilo counts
70
OKLL
50
CKLL
CIs
30
AI2p AI2s
10
0
0
100
200
300
600
400
500
Binding energy (eV)
700
800
900
Figure 7.2 XPS spectrum of an oxidized aluminum surface. (Reproduced with permission
from Ref. [1]. © 1990 Royal Microscopy Society.)
excited state. The atom will quickly return to its normal state after refilling the
inner electron vacancy with an outer-shell electron. In the meantime, the energy
difference between the outer-shell electron and the inner shell may cause emission
of either an Auger electron from an electron shell or a characteristic X-ray photon.
The kinetic energy of an Auger electron is approximately equal to the energy
difference between the binding energies in the electron shells involved in the
Auger process. For example, the kinetic energy of an Auger electron in Figure 7.1b
is approximated by the following equation.
EKL1 L2,3 ≈ EBK − EBL1 − EBL2,3
(7.2)
The notation for the kinetic energy of Auger electrons describes its origin, but the
nomenclature is rather complicated. For example, the kinetic energy of an Auger
electron in Eq. (7.2) is from a process illustrated in Figure 7.1b; that is, an incident
electron knocks out a K-shell electron, a L1 -shell electron refills the K-shell vacancy,
and a L2.3 -shell electron is ejected as the Auger electron. The subscript of E BX
indicates the binding energy of electron shell X; for example, E BK is the binding
energy of the K shell. AES identifies chemical elements by measuring the kinetic
energies of Auger electrons. In an AES spectrum, an individual kinetic-energy
peak from an Auger electron is marked with an elemental symbol and subscripts
indicating the electron shells or subshells involved, for example, Al KLL , OKLL , and
so on. A typical AES spectrum is a plot of intensity versus kinetic energy; most
commonly, it is a plot of the first derivative of intensity versus the kinetic energy,
as shown in Figure 7.3.
1000
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7.1 Basic Principles
7 Electron Spectroscopy for Surface Analysis
AI KLL
(a)
O KLL
C KLL
(b)
200
400
600
800
1000
1200
1400
1600
1800
2000
Kinetic energy (eV)
Figure 7.3 AES spectra of an oxidized aluminum surface: (a) direct spectrum of intensity
versus kinetic energy of Auger electrons and (b) differential spectrum of intensity versus kinetic energy of Auger electrons. (Reproduced with permission from Ref. [1]. © 1990 Royal
Microscopy Society.)
The Auger peaks appear small against the background of the direct mode
spectrum. This occurs because the signals from Auger electrons are relatively
weak compared with those of secondary electrons that have escaped from a solid
surface. The interactions between incident electrons with material atoms are
discussed in Chapter 4. Recalling Figure 4.10, electrons are either elastically or
inelastically scattered when a primary electron beam strikes a solid. Figure 7.4
illustrates numbers of Auger electrons compared with numbers of other electrons
that escape from a solid surface. The primary electrons ejected from a solid surface
by inelastic scattering comprise the background of an AES spectrum in the region
of high kinetic energies, while the secondary electrons comprise the background
in the region of low kinetic energies. The number of Auger electrons ejected from
a sample is much less than that of scattered primary electrons and secondary
electrons. Thus, the direct-mode spectrum is not favored, except for quantitative
analysis.
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224
True secondary
electrons
N(E)
III
Auger electrons
Elastic peak
Plasmon losses
II
0
400
800
1200
1600
Electron energy (cV)
2000
E0
Figure 7.4 Schematic comparison of Auger peak intensity with other electrons escaped
from a solid surface. Eo indicates energy of incident electrons. The kinetic energy of electrons can be divided into three regions I, II, and III from low to high. (Reproduced with
permission from Ref. [2]. © 2006 John Wiley & Sons.)
7.2
Instrumentation
A modern instrument for electron spectrometry contains both XPS and AES in a
single chamber as a multifunctional surface analysis system. A scanning electron
microscope (SEM) system may also be included in order to image the microscopic
area to be examined by electron spectroscopy. Figure 7.5 schematically illustrates
a system combining AES and XPS, which includes an electron gun, an X-ray
gun, and a shared analyzer of electron energy. The electron beam for generating
the Auger electron emission can be easily focused and scanned over a sample
surface to obtain two-dimensional mapping for AES analysis. Thus, AES analysis
is commonly the scanning type, called scanning Auger microscopy.
7.2.1
Ultrahigh Vacuum System
Instruments for electron spectrometry require an ultrahigh vacuum environment
with a vacuum pressure in the range 10−8 –10−10 mbar (1 mbar = 100 N m−2
= 1.33 torr). Reasons for such a high vacuum are to reduce the chances of lowenergy electrons being scattered by gas molecules on their way to reach the detector,
and to keep the sample surface free from gas-molecule contamination. Low-energy
photoelectrons and Auger electrons are easily scattered by gas molecules. Scattering
will reduce signal intensity and increase background noise in spectra. Surface
contamination by gas molecules is a major concern for surface chemical analysis. It
is possible for a surface to adsorb a monolayer of gas molecules within one second
225
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7.2 Instrumentation
Lens voltage
+Hemisphere voltage
Retarding voltage
Channel
electron
multiplier
Hemispherical
sector
analyzer
Electrostatic
transfer lens
Analyzer entrance
and exit slit plate
n
El
n
gu
Ratemeter
ec
n
tro
Io
ng
un
Amplifier
y
-ra
gu
X
e−
θ
Recorder Y
Specimen
Analysis chamber
C.P.S.
Recorder X
High voltage
−Hemisphere voltage
Spectrometer control unit
Electron energy
X-Y recorder
Figure 7.5 Structure of an electron spectrometer. (Reproduced with permission from
Ref. [1]. © 1990 Royal Microscopy Society.)
in a vacuum environment of 10−6 mbar. However, the typical time to collect XPS
and AES spectra is more than several hundred seconds. Only an ultrahigh vacuum
environment ensures satisfactory analysis, particularly for surfaces containing
elements that exist in gaseous environments such as C, O, and N.
The ultrahigh vacuum chamber is commonly made from stainless steel, and
joints of chamber parts are made from crushed copper gaskets. Ultrahigh vacuum
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7 Electron Spectroscopy for Surface Analysis
226
pressure can be achieved using diffusion pumps, sputter ion pumps, or turbomolecular pumps. Currently, sputter ion pumps and turbomolecular pumps are
more commonly used than diffusion pumps that may contaminate the chamber by
leaking oil gas molecules.
Vacuum pumping alone cannot achieve the necessary ultrahigh vacuum because
gas molecules will come from the internal chamber walls in such a low-pressure
environment. Thus, the vacuum chamber must be baked at an elevated temperature
(250–350 ◦ C) and pumped. This baking process allows the gas molecules adsorbed
onto the chamber walls to be pumped out. An additional requirement for the
chamber is magnetic shielding, because the trajectory of signal electrons is strongly
affected by any magnetic field, even the Earth’s magnetic field.
7.2.2
Source Guns
7.2.2.1 X-Ray Gun
An electron spectrometer system contains an X-ray gun for XPS analysis. The
working principles of the X-ray gun are similar to the X-ray tube used for X-ray
diffractometry introduced in Chapter 2. X-ray photons are generated by high-energy
electrons striking a metal anode, commonly Al or Mg for XPS spectrometry. The
X-ray gun produces a characteristic X-ray line to excite atoms of the surface to be
analyzed. XPS uses both nonmonochromatic and monochromatic X-ray sources.
The output from a nonmonochromatic X-ray source consists of a continuous
energy distribution with high intensity of Kα characteristic lines, as shown in
Figure 7.6. The output of the monochromatic source is produced by removing
106
Aluminum 15 kV
Logarithmic intensity plot
105
Counts
104
103
102
10
1
0
5
10
15
Photon energy, keV
Figure 7.6 Nonmonochromatic X-ray radiation from an X-ray gun with an Al target. The
characteristic Al Kα line is at about 1.5 keV. (Reproduced with permission from Ref. [3]. ©
2003 IM Publications.)
227
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7.2 Instrumentation
7 Electron Spectroscopy for Surface Analysis
Cooling water
Focusing
shields
Filament 1
Filament 2
e−
Anode face 1
AI window
Figure 7.7 An X-ray gun with two anodes. Two tapered anode faces (one is
Al and the other is Mg) have semicircular filaments, which are near ground potential. An acceleration voltage of about
hv
Anode face 2
15 kV between a filament and anode generates X-rays that exit through an Al
window. (Reproduced with permission
from Ref. [4]. © 1990 John Wiley & Sons
Ltd.)
continuous X-rays from a radiation spectrum. The monochromatic source is useful
for obtaining XPS spectra with reduced background intensity.
Energies of the characteristic X-ray lines used in XPS are lower than those used
in X-ray diffractometry. For example, the energies of AlKα and MgKα are 1.4866
and 1.2536 keV, respectively; however, the energies of CuKα and MoKα, which are
commonly used in X-ray diffractometry, are 8.04 and 17.44 keV, respectively. The
reason to choose lower-energy X-rays, also called ‘‘soft’’ characteristic X-rays, is their
narrow line width. The line width of characteristic X-rays refers to their range of
energy. XPS requires a line width less than 1.0 eV to ensure good energy resolution.
Both AlKα and MgKα exhibit line widths less than 1.0 eV and also have sufficient
energies (>1000 eV) for photoelectron excitation. Different from the X-ray tube
used in an X-ray diffractometer, many XPS instruments use a dual-anode X-ray
gun, a single X-ray gun with both Al and Mg anodes. The structure of a dual-anode
X-ray gun is schematically shown in Figure 7.7. Such a gun structure makes
switching between AlKα and MgKα simple. However, high energy resolution XPS
instruments commonly are fitted with a monochromatic AlKα source.
7.2.2.2 Electron Gun
The electron guns used in AES analysis is similar to those used in electron
microscopy. LaB6 and field emission guns are commonly used in electron spectrometers. The LaB6 gun can provide an electron beam of high brightness with
spatial resolution of 200 nm after being focused by an electromagnetic lens.
Field emission guns are increasingly used in modern instruments. These guns
provide superior brightness and higher spatial resolution than LaB6 ; in addition,
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228
their emitting surface remains clean during operation without adsorption of gas
molecules.
7.2.2.3 Ion Gun
An electron spectrometer is also equipped with an ion gun, as shown in a system
combining AES and XPS (Figure 7.5). The functions of an ion gun are twofold. First,
it provides a high-energy ion flux to clean sample surfaces before examination. This
is necessary because the signal electrons come from the surface atom layers of a
sample. Sample surfaces are commonly contaminated with adsorbed hydrocarbons,
water vapor, and oxides that need to be removed before surface analysis. Secondly,
it sputters out sample atoms layer by layer so that an elemental depth profile can
be revealed. The ion gun produces an argon ion beam by either electron impact
or gaseous discharge. This beam has an energy level of 0.5–5.0 keV, and can be
focused to a diameter down to several tens of micrometers. The ion beam can scan
a surface area as large as 10 × 10 mm. The ion gun will be discussed in more detail
in Chapter 8 with secondary ion mass spectroscopy.
7.2.3
Electron Energy Analyzers
An electron spectrometer relies on an electron energy analyzer to obtain XPS and
Auger spectra. The most commonly used analyzer is the concentric hemispherical
analyzer (CHA), also called the hemispherical sector analyzer (HSA) as shown in
Figure 7.5. The analyzer is composed of two concentric hemispheres with radii R1
and R2 and its working principles can be understood from the schematic illustration
in Figure 7.8. Negative potentials V 1 and V 2 are applied to the inner and outer
hemispheres, respectively. The applied potential generates a median equipotential
(=V o ) surface with radius of Ro . A slit at one end of the CHA allows electrons from
the sample to enter, and a slit at the other end lets electrons pass through to an
electron detector. The CHA only allows the electrons with energy E o = eV o (called
the pass energy of CHA), which are injected tangentially to the median surface, to
pass through its channel and reach the detector.
Before being injected into the CHA, electrons are focused by an electrostatic
transfer lens, and their energies are reduced to a certain level. Electron energy
reduction by electrostatic processing is called electron retardation. The electrons
can be analyzed by one of two modes: the constant analyzer energy (CAE) mode or
constant retarding ratio (CRR) mode. Commonly, the spectrometer is run in the
CAE mode for XPS and in the CRR mode for Auger spectroscopy. The CAE mode
maintains the pass energy of the CHA as a constant. Electron energies are analyzed
by recording the change of electron retardation. The CRR mode maintains the
ratio of electron retardation as a constant and the electron energies are analyzed by
recording the change of pass energy.
It is necessary to have knowledge of electron energy resolution and CHA characteristics
to understand the reasons for using different modes. Electron energy resolution can be
expressed either in an absolute form (E) or in a relative form (E/E). XPS requires
229
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7.2 Instrumentation
7 Electron Spectroscopy for Surface Analysis
V2
R2
R0
V1
R1
To detector
Figure 7.8
From sample
Working principles of a concentric hemispherical analyzer.
high absolute resolution of about 0.5 eV in the whole range of a spectrum. However, the
CHA has a relative resolution limit, which is determined by the geometric configuration
of the CHA, including such factors as hemisphere radii and slit opening. A resolution
of 0.5 eV is readily achievable when the photoelectron energy is low because the relative
resolution is also low. For example, for E = 200 eV, a CHA requires a relative resolution
of 0.025 to satisfy the XPS absolute resolution of 0.5 eV. However, for E = 1500 eV, a
CHA requires a relative resolution of 0.003 to do so, which is not practical. Thus, to
ensure absolute resolution in a whole spectrum range, XPS analysis requires retarding the
electron energy to achieve a low CHA pass energy, commonly 10–100 eV. For example,
a photoelectron with energy of 1000 eV will be retarded to a pass energy of 50 eV. An XPS
spectrum is recorded by changing the retarding electric potential in the CAE mode.
Auger analysis requires suppression of the electron signal at the low-energy end of
its spectrum. The CRR mode meets the Auger analysis requirement because the CHA
exhibits a low transmission rate with low pass energy. When a constant retardation ratio
is applied, a low Auger electron energy generates low CHA pass energy. For example,
with a retardation ratio of 10, the pass energy is only 10 eV for E = 100 eV, while the
pass energy is 100 eV for E = 1000 eV. In other words, electron transmission through a
CHA is lower at a pass energy of 10 eV than at 100 eV. An Auger spectrum is commonly
recorded by changing the CHA pass energy in the CRR mode.
7.3
Characteristics of Electron Spectra
7.3.1
Photoelectron Spectra
XPS spectra are expressed as photoelectron intensity versus binding energy (E B )
as shown in Figure 7.9. An XPS spectrum can have three types of peaks on a
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230
231
3d
MNN
3p
4d
3s
4s
4p
x4
1000
Binding energy, eV
0
254
Kinetic energy, eV
1254
Figure 7.9 An XPS spectrum of silver excited Mg Kα with a pass energy of 100 eV. (Reproduced with permission from Ref. [4]. © 1990 John Wiley & Sons Ltd.)
background: photoemission from core electron levels, photoemission from valence
levels, and Auger emission excited by X-rays. Figure 7.9 shows an XPS spectrum of
a clean silver surface in which the core-level peaks are marked as 3s, 3p, and 3d; the
valence-level peak is marked as 4d and the Auger peaks are marked as MNN. The
core-level photoelectron peaks are the primary peaks for elemental analysis. The
valence-level peaks are those at low binding energy (0–20 eV) and are primarily
useful in studies of the electronic structure of materials. The Auger peaks, arising
from X-rays excited in the Auger process, are also useful for chemical analysis.
XPS spectra have a step-like background, increasing with binding energy. They
result from inelastic scattering of photoelectrons in a solid. It should be noted that
the X-ray radiation is commonly not exactly monochromatic. The photoelectron
emission can also be excited by continuous X-rays, which are commonly associated with characteristic X-ray radiation. Such photoelectron emission generates a
background in the low binding energy region of the spectrum. The XPS spectrum
can also include extra, or satellite, peaks associated with a main core-level peak, as
shown in Figure 7.10.
Shake-up satellites are the extra peaks that result from interaction between a
photoelectron and a valence electron. A photoelectron can excite (shake-up) a
valence electron to a higher energy level and thereby lose a few electron volts of
kinetic energy. This will create a satellite peak associated with a core-level peak
of photoelectrons as shown in Figure 7.10a. For certain transition and rare-earth
metals with unpaired electrons in 3d and 4f shells, the shake-up satellites produce
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7.3 Characteristics of Electron Spectra
7 Electron Spectroscopy for Surface Analysis
Copper (II) oxide
'Shake up' satellites
Cu 2p
925
Cu 2p 1
3
2
2
935
945
955
Binding energy (eV)
(a)
Nickel (II) oxide
Multiplet splitting
of Ni 2p 3
2
975
965
'Shake-up' satellites
Ni 2p 1
2
855
860
(b)
865
870
875
880
Binding energy (eV)
885
890
Aluminum
AI 2p
AI KLL Auger
AI 2p plasmon
Ka3,4
60
(c)
70
80
Binding energy (eV)
90
100
Figure 7.10 Examples of several types of satellite peaks in XPS spectra: (a) shake-up peaks
in a CuO spectrum; (b) shake-up peaks and multiplet splitting in a NiO spectrum; and (c)
plasmon loss peak in a clean Al spectrum. (Reproduced with permission from Ref. [1]. ©
1990 Royal Microscopy Society.)
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232
strong peaks. Organic materials with aromatic systems also show shake-up satellites
with intensities up to approximately 10% of core-level peaks. Shake-up satellites
are useful for chemical analysis. For example, a shake-up satellite is associated with
the Cu 2p of CuO, but it is absent around the Cu 2p peak of Cu2 O.
Multiplet splitting of a core-level peak may occur in a compound that has unpaired
electrons in its valence level. For example, the core-level peak of Ni 2p 3 of NiO in
2
Figure 7.10b shows multiplet splitting. Detailed explanation of multiplet splitting
involves knowledge of quantum theory of electron structure, which is beyond the
scope of this book. Multiplet splitting is also useful in chemical analysis. For
example, Ni(OH)2 can be distinguished from NiO because the 2p 3 of Ni(OH)2
2
does not have multiplet splitting.
Plasmon loss generates another type of satellite peaks; these peaks do not provide
useful information but they complicate a spectrum. Plasmon loss refers to the
kinetic energy loss of a photoelectron because it excites collective vibrations in
conduction electrons in a metal. The vibrations require a characteristic amount of
energy. Such characteristic amounts of photoelectron energy loss in photoelectrons
will generate satellite peaks, as shown in Figure 7.10c. Plasmon loss peaks are
shown in XPS spectra of clean metal surfaces and also in Auger spectra.
7.3.2
Auger Electron Spectra
Auger spectra can be expressed in two modes: a direct mode and differential mode,
as shown in Figure 7.3. The direct mode presents the intensity distribution in a
range of electron kinetic energies. The differential mode presents the derivative
of intensity versus the kinetic energy. The differential mode is more widely used
because the Auger peaks are more obvious than in the direct mode. Figure 7.11
shows the Auger spectra of a contaminated tungsten foil as an example. The CRR
mode of the CHA generates a constant relative resolution (E/E) over the whole
range of the spectrum. The direct mode spectrum acquired with the CRR mode
expresses the energy distribution as the number of electrons multiplied by its
kinetic energy, EN(E), as shown in Figure 7.11a.
The differential mode spectrum is produced by taking the first derivative of
the curve in the direct mode using computer software. The ordinate should be
d(EN(E))/dE in the differential mode spectrum with the CRR acquisition, as
shown in Figure 7.11b. The differential mode effectively reduces the background
and enhances the Auger peaks. The Auger energy in the differential mode is
represented by a sharp minimum position corresponding to an Auger signal. For
example, Figure 7.12 shows the energy of the carbon KLL line is 272 eV in the
differential mode; however, this energy is not exactly identical to the carbon KLL
peak energy in the direct mode. It is slightly higher because the exact peak energy
in the direct mode should equal that of the differentiated curve passing zero. In
practice, such a difference is often ignored for element identification.
A light element is often identified from its KLL Auger lines, which dominate in
the Auger spectrum range. However, for an element with atomic number higher
233
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7.3 Characteristics of Electron Spectra
7 Electron Spectroscopy for Surface Analysis
W
EN(E)
WC N O
W
0
500
(a)
1000
1500
2000
Kinetic energy (eV)
O
WC N
P
W
d [EN(E)]/dE
W
0
(b)
500
1000
1500
2000
Kinetic energy (eV)
Figure 7.11 Auger spectra of a contaminated tungsten foil acquired in a fixed retarding ratio mode with 0.6% relative resolution: (a) direct spectrum and (b) differential spectrum.
Elements P, N, O, W, C are indicated. (Reproduced with permission from Ref. [3]. © 2003
IM Publications.)
than 15, either LMM or MNN Auger lines are dominant. Figure 7.13 is a chart
of the principal Auger electron energies for different elements. The LMM lines
for an element are divided into three, as triplets. The LMM triplet feature results
from the difference in subshells involved in the Auger process. Figure 7.14 shows
triplet spectra of three transition metals. In iron, for example, triplet lines at 703,
651, and 598 eV correspond to the Auger processes of L3 M45 M45 , L3 M23 M45 , and
L3 M23 M23 , respectively. The KLL Auger electrons can also result from more than
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234
N
235
O
F
C
Na
B
Be
348
600
468
923
621
360
963
951
483
990
647
179
104
272
379
0
100
200
300
400
503
500
600
700
900
1000
Kinetic energy, eV
Figure 7.12 Principal Auger KLL peaks of light elements, Be, B, C, N, O, F, and Na. KL23
L23 is the most visible KLL peak for each element; for example, OKL1 L1 (468 eV), OKL1 L23
(483 eV), and OKL23 L23 (503 eV). (Reproduced with permission from Ref. [4]. © 1990 John
Wiley & Sons Ltd.)
one Auger process and produce several KLL lines including KL1 L1 , KL1 L23 , and
KL23 L23 ; however, KL23 L23 is dominant, as shown in Figure 7.12. Understanding
such characteristics of Auger peaks is necessary in identifying chemical elements
from Auger spectra.
7.4
Qualitative and Quantitative Analysis
7.4.1
Qualitative Analysis
XPS and AES are powerful tools for surface chemical analysis. They can identify
chemical elements in the layer within several nanometers from the surface.
Importantly, peak positions of elements in XPS and AES spectra are sensitive to
their chemical status; for example, carbon peak positions in CO2 are different from
those in saturated hydrocarbons. This phenomenon, called the chemical shift in
XPS and AES spectra, provides extra information for chemical analysis. Also, XPS
and AES instruments are able to generate depth profiles of the chemistry of the
1100
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
Principal auger electron energies
Dots indicate the electron energies of the principal auger
peaks for each element: Large dots represent predominant
peaks for each element.
85
80
75
70
MNN
65
60
55
Atomic number
U
Th
Ac
Ra
Fr
Rn
At
Po
Bi
Pb
Ti
Hg
Au
Pt
Ir
Os
Re
W
Ta
Hf
Lu
Yb
Tm
Er
Ho
Dy
Tb
Gd
Eu
Sm
Pm
Nd
Pr
Ce
La
Ba
Cs
Xe
I
Te
Sb
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
Co
Fe
Mn
Cr
V
Ti
Sc
Ca
K
Ar
CI
S
P
Si
AI
Mg
Na
Ne
F
O
N
C
B
Be
Li
He
H
Pa
90
50
45
40
LMM
35
30
25
20
KLL
15
10
5
0
200
400
600
800 1000 1200 1400 1600 1800 2000 2200 2400
Electron energy (eV)
Figure 7.13 Chart of principal Auger electron energies of KLL, LMM, and MNN lines.
(Reproduced with permission from Ref. [1]. © 1990 Royal Microscopy Society.)
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236
482
571
Chromium
489 529
36
535
Manganese
636
542 589
40
591
Iron
598
651 703
47
0
100
200
300 400 500
Kinetic energy, eV
600
700
800
Figure 7.14 Triplet peaks of Auger spectra for Cr, Mn, and Fe. The LMM triplets occur in
transition metals. The low kinetic energy peaks are of L2,3 VV, where V represents the level
of valence electrons. (Reproduced with permission from Ref. [4]. © 1990 John Wiley & Sons
Ltd.)
surface layer of bulk materials and reveal the spatial distributions of elements on
the surface of bulk materials.
Peak identification in spectra is the primary task in qualitative analysis. For
example, data in Figure 7.13 can be used to identify peaks in AES spectra. Table 7.1
lists the binding energies of elements in core levels. Such energies are the primary
source for peak identification of XPS spectra. Peak identification is a nontrivial
task in electron spectroscopy such as XPS. In additional to the spectrum features
discussed in the previous section, other factors such as chemical shift and surface
237
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
Table 7.1
Z
XPS peak positions of elements irradiated with Al X-rays.
Element 1s 1
2
K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
42
46
48
73
79
a
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Mo
Pd
Ag
Taa
Aua
2s 1
2
L1
2p 1
2
L2
2p 3
3s 1
3p 1
3p 3
3d 3
3d 5
L3
M1
M2
M3
M4
M5
2
2
2
14
25
55
111
188
5
284
6
399
9
532
24
7
686
31
9
867
45
18
1 072
63
31
1
1 305
89
52
2
1 560
118
74
73
1
1 839
149
100
99
8
2 149
189
136
135
16
10
2 472
229
165
164
16
8
2 823
270
202
200
18
7
3 202
320
247
245
25
12
3 608
377
297
294
34
18
4 038
438
350
347
44
26
4 493
500
407
402
54
32
4 965
564
461
455
59
34
5 465
628
520
513
66
38
5 989
695
584
757
74
43
6 539
769
652
641
84
49
7 114
846
723
710
95
56
7 709
926
794
779 101
60
8 333
1 008
872
855 112
68
8 979
1 096
951
932 120
74
9 659
1 194
1 044
1 021 137
90
10 367
1 299 1 144
1 117 160
106
20 000 2 866 2 625
2 520 505 410
24 350 3 604 3 330
3 173 670 559
25 514
3 806 3 523
3 351 718 602
67 416 11 681 11 136
11 544 566a 464a
80 724 14 352 13 733
14 208 763a 643a
2
2
2
5
7
3
2
2
4
6
3
4
2
9
20
393
531
571
403a
547a
4s, 4p, and 4f levels indicated, respectively.
Z, atomic number.
Data reproduced with permission from Ref. [5]. © 1997 John Wiley & Sons Ltd.
208
340
373
24a
88a
205
335
367
22a
84a
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238
charge can complicate peak identification. The following section briefly reviews the
important factors that, particularly for XPS, affect peak identification.
7.4.1.1 Peak Identification
Peak identification in AES spectra is straightforward. The peaks in an AES spectrum
can be identified by comparing the experimental peaks with standard peaks found
in reference books or computer databases. Peak identifications in XPS spectra,
however, are more complicated because Auger peaks may be present. We use two
different X-ray sources to distinguish the Auger peaks from photoelectron peaks.
An Auger peak represents the kinetic energy of an Auger electron that changes
with energy of primary X-rays. Thus, an Auger peak will shift in apparent binding
energy in an XPS spectrum when we change the X-ray source. For example, an
Auger peak shifts by 233 eV in the XPS spectrum when we change the radiation
from MgKα(1253.6 eV) to AlKα(1486.6 eV).
Peak positions in an XPS spectrum are likely to be affected by spectrometer
conditions and the sample surface. Before XPS peak identification, we often need
to calibrate the binding energy. Calibration is particularly important for samples
with poor electrical conductivity. Calibration can be done with an internal standard
that has a peak that shows little or no chemical shift, for example, elemental Si.
The most common method is use of the C 1s peak at 285 eV from carbon adsorbed
on the sample surface. The carbon from organic debris (as C–H or C–C) in air is
found on all samples exposed to the environment. The peaks of core-level binding
energies, as listed in Table 7.1, are sufficiently unique for element identification.
7.4.1.2 Chemical Shifts
Chemical shifts of binding-energy peaks for an element are caused by the surrounding chemical state of the element. Knowing possible chemical shifts is necessary to
identify the peaks correctly. We can use the features of chemical shifts to identify
not only elements but also chemical compounds. For example, Figure 7.15 shows
the XPS spectrum of poly(vinyl trifluoroacetate) (PVTFA). The carbon atoms in different environments generate distinctive peaks as shown in Figure 7.15a. Similarly,
oxygen atoms in two different environments also generate two peaks as shown in
Figure 7.15b. The XPS spectra shown in Figure 7.15 with defined peak positions
and relative peak intensities can also be used as a fingerprint to identify PVTFA.
Small shifts in binding energy may cause peak overlap as shown in Figure 7.15b.
Thus, we often need to carefully resolve the overlapped peaks with assistance of
computer software.
The chemical shifts of the C 1s peak are summarized in Figure 7.16. The
range of the C 1s shift extends over 12 eV. We can identify the different carbon
bonds according to the amounts of chemical shifts. The binding-energy difference
between C–C and C=O is about 3 eV. This is extremely useful for identifying
polymers by revealing various carbon bonds. Chemical shifts can also reveal
the degree of oxidation in molecular solids. The larger the number of electrons
transferred, the higher the chemical shift. Chemical shifts are less obvious in
239
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
2000
O
1s
Counts
1500
4
2
3
1
1000
500
0
295
290
Binding energy [eV]
(a)
5000 O
285
1s
4000
Counts
2
1
3000
2000
1000
0
538
(b)
536
534
532
Binding energy [eV]
530
528
Figure 7.15 XPS spectrum of poly(vinyl trifluoroacetate): (a) C 1s and (b) O 1s with
monochromatic Al Kα excitation. (Reproduced with permission from Ref. [3]. © 2003 IM
Publications.)
metallic and semiconductive elements because the shifts decrease with increasing
atomic number. For example, the shift range of Si 2p is less than 6 eV.
Chemical shifts also occur in AES spectra, and the chemical shifts can be
significantly larger than the shifts in XPS. For example, the shift between metallic
and oxide Al peaks of AlKL2 L3 is more than 5 eV, while the corresponding shift of
Al 2p binding energy is only about 1 eV. In addition, Auger peak shape may be
affected by the chemical state. For example, Figure 7.17 shows the position and
shape of oxygen KLL Auger peaks in different types of oxides. Separation between
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240
1st Binding energy (eV)
Compound type
280
282
284
286
288
290
292
294
Carbide
Carbon
C with N
C with S
C with O
Alcohols
Ethers
Ketones/Aldehydes
Carboxyls
Carbonates
C with CI
C with F
CHF
CF2
CF3
Figure 7.16 Chart of carbon chemical shift in XPS spectra. (Reproduced with permission
from Ref. [3]. © 2003 IM Publications.)
the OKL1 L23 and OKL23 L23 peaks varies by up to 5 eV and the shape of the OKL23 L23
peak also varies between a single and a double type.
7.4.1.3 Problems with Insulating Materials
We may find that peak positions in the spectra of insulating materials do not match
well with standards provided in handbooks. To understand this phenomenon in
XPS, we have to know more about the basic equation for binding-energy calculation
(Eq. (7.1)). For a conducting sample that electrically contacts with a spectrometer,
in Eq. (7.1) will be a work function of the spectrometer and its value is a constant
(∼4.5 eV). For an insulating sample, however, is not certain and it is related
to the surface potential of the sample. Photoelectron emission from an insulating
sample results in build-up of positive charge on the sample surface. This build-up
will change the surface potential of the sample during XPS data collection. Also,
the surface of an insulating sample tends to charge negatively in AES because
incident electrons cannot be removed by electrical conduction. A change of surface
potential can make the measured kinetic energy or binding energy tens of electron
volts different from a standard value in a published table.
The method used to control the surface potential problem is charge neutralization.
This is performed in order to provide a stable and uniform surface potential on the
solid. In XPS, the sample surface is provided with a flux of low-energy electrons
using an electron flood gun as shown in Figure 7.18. The electron flux compensates
for charge loss due to photoelectrons escaping from the surface. The flux helps
maintain a stable surface potential. Figure 7.19 shows the differences in XPS
spectra of a polymer sample with and without charge neutralization. In performing
XPS examination of insulating samples, the surface-charge problem is much more
241
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
KNO3
NaOAc
N2H6SO4
Na2WO4
TiO2
20 eV
Figure 7.17 Comparison of positions and shapes of O KLL Auger peaks in several solid
oxides. (Reproduced with permission from Ref. [4]. © 1990 John Wiley & Sons Ltd.)
Electron
flood gun
Low-energy
electrons
X-rays
Photoelectrons
Sample
Figure 7.18 Compensating the electron loss due to photoelectron escape using low-energy
electron flux from a flood gun.
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242
Electron counts
C
(c) Flood gun
optimized
(scale x 0.5)
O
Si
0
(b) Flood gun on
0
120 eV
(a) Flood gun off
0
1000
800
600
400
Binding energy (eV)
Figure 7.19 Comparison of XPS spectra of plastic tape with a monochromatic
X-ray source: (a) spectrum with electron flood gun off; (b) spectrum with the
flood gun on, but with incorrect electron
200
0
compensation; and (c) spectrum with
the flood gun on and proper electron compensation. (Reproduced with
permission from Ref. [3]. © 2003 IM
Publications.)
severe with monochromatic than with nonmonochromatic X-ray radiation. The
reason is that nonmonochromatic X-rays illuminate the window of the X-ray gun as
well as other surfaces inside the vacuum chamber, producing sufficient secondary
electron flux to neutralize the positively charged sample surface. Hence, using
nonmonochromatic X-rays has much the same effect as using an electron flood
gun.
For AES, this surface-charge problem with insulating samples is more difficult
to overcome because the electrons have to be removed from the insulating surface,
instead of compensating for electron loss. AES does not work well with totally
insulating materials. Commonly used methods in AES for reducing surface charge
are reduction of the primary electron beam energy and the application of a
conductive coating. The surface potential can be stabilized when the energy of the
primary electron beam is reduced, for example, from 10 to about 2–5 keV. We also
can coat the surface near the area (but not in the area) to be examined with a thin
layer of metal such as silver or gold to achieve the same effect.
Composition Imaging AES and XPS can also be used to analyze the distributions
of chemical elements on surfaces by producing compositional maps, similar
to the energy dispersive spectrometer (EDS) mapping discussed in Chapter 6.
Composition imaging with AES is obtained by scanning the sample surface
with a focused electron beam. The spatial resolution of the composition maps
mainly depends on the diameter of the beam. Auger imaging is a well-developed
technique because focusing the electron beam is readily obtained with the use
243
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
10 µm
10 µm
10 µm
10 µm
10 µm
Figure 7.20 Comparison between images of gold-coated stainless steel: (a) a scanning
electron microscope (SEM) secondary electron image; (b) iron Auger image; (c) oxygen
Auger image; (d) gold Auger image; and (e) nickel Auger image. (Reproduced with permission from Ref. [4]. © 1990 John Wiley & Sons Ltd.)
of an electromagnetic lens. The diameter of the electron beam can be as small
as ∼10 nm when a field emission gun is employed. Figure 7.20 shows examples
of AES images obtained from a surface area of a gold-coated stainless steel lead
frame. The grain structure is revealed by the secondary electron image (Figure
7.20a). The Auger images disclose the presence of iron, oxygen, gold, and nickel on
the steel surface. The iron and oxygen on the surface are concentrated along grain
boundaries. Nickel is diffused around grain boundaries.
Composition imaging with XPS is a more difficult task than with AES because an
X-ray photon beam that is electrically neutral cannot be focused by electromagnetic
lens as an electron beam. Modern XPS instruments use either scanning or parallel
optics to generate imaging. The scanning method utilizes a focused monochromatic
X-ray beam to scan over an area of specimen. The X-ray beam is focused by an
X-ray monochromator based on the Bragg diffraction geometry that is schematically
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244
Crystal
Electron
beam
X-ray
X
an -ray
od g
e un
en
im
c
pe
S
Figure 7.21 Schematic illustration of focusing X-ray beam for XPS composition map. The
beam generated from an X-ray gun is focused by a curved crystal. The scanning the beam
on a specimen surface is realized by a scanning electron beam on the anode surface of the
gun.
100 µm
(a)
100 µm
(b)
Figure 7.22 XPS images of a TiAlN thin film on a stainless steel substrate: (a) Ti 2p photoelectron image and (b) Fe 2p photoelectron image. (Reproduced with permission from
Ref. [3]. © 2003 IM Publications.)
shown in Figure 7.21. The scanning mechanism is realized in a special arrangement
in an X-ray gun by using a focused electron beam to scan over a metal anode to
a scanning X-ray beam. After being focused by the X-ray monochromator, such a
beam can scan over an area of a specimen. This scanning type of XPS imaging
can obtain a lateral resolution of ∼10 μm. The parallel imaging method, however,
can achieve a better resolution (∼3 μm). The optical principle of parallel imaging
is somewhat similar to that of electron microscopes. A whole macroscopic area
is illuminated by an X-ray beam simultaneously. Photoelectrons from the whole
area are imaged simultaneously by electromagnetic lenses of optical systems at the
entrance and at the exit of an energy analyzer. The resolution limit is controlled by
lens aberrations of the optical systems. Figure 7.22 shows examples of XPS images
obtained from a surface area of oxidized TiAlN film on stainless steel substrate.
The oxidized film contains iron that has migrated from the substrate. The spatial
resolution of XPS images is generally poorer than that of AES images.
245
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
7.4.2
Quantitative Analysis
7.4.2.1 Peaks and Sensitivity Factors
Quantitative elemental analysis in electron spectroscopy is similar to that in X-ray
spectroscopy. Analysis quantifies the concentrations of chemical elements on a
sample surface from the peak intensities of the spectra. In theory, the quantitative
relationship between the intensities of electron signals and atomic fractions of
elements can be calculated. In practice, for quantification in both XPS and AES,
most parameters for calculations are not available. Thus, the following empirical
equation is commonly used.
I /S
Xi = i i
Ij /Sj
(7.3)
An atomic fraction of a surface element (Xi ) can be calculated from knowing its
peak intensity (Ii ) and sensitivity factor (Si ). The sensitivity factor for each element
is experimentally determined and varies with the conditions of the instrument
and sample surface. It is desirable to measure the sensitivity factor for a given
spectrometer and sample type. Common practice is to use the sensitivity factors
from published handbooks with certain corrections according to the instrument
characteristics, because it is not feasible to compile a set of in-house sensitivity
factors. For example, Figure 7.23 shows the Auger sensitivity factors of elements
published in a handbook of Auger electron spectroscopy. The sensitivity factors are
values relative to that of the CuLMM Auger line, which is set as unity. Also, note
the sensitivity factors in Figure 7.23are only useful for a primary electron energy of
10 keV.
The quantitative calculations based on Eq. (7.3) include assumptions and approximations. The calculations can readily lead to erroneous results unless caution
is exercised. The intensities of XPS peaks should be calculated from the peak
areas after subtracting the background. The intensity of AES peaks should be the
peak-to-peak height in differential spectra. Unfortunately, the peak-to-peak heights
may vary with instrument resolution and the differentiation (modulation) process.
This problem may be resolved by using the AES direct spectrum. However, the
relative intensities of peaks to background are low. Small errors in background
subtraction can generate large variation in peak-height measurement.
The published sensitivity factors are obtained with specific instruments and
standard samples of pure elements. Sensitivity factors are subject to change
with different samples and developments in instruments. For example, chemical
contamination on a sample surface affects the accuracy of using Eq. (7.3). For an
AES spectrum, the matrix composition affects the efficiency of Auger emissions
because the backscattered electrons in the matrix also excite Auger electron
emission. Thus, we expect that the intensity of element i in a matrix with multiple
elements differs from that of the same amount of i element in its pure solid state.
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246
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
247
90
10.00
1.00
1.00
Sensitivity factor
10.00
KLL
LMM
MNN
0.10
0.10
0.01
0.01
0
5
10
15
20
25
30
35
40 45 50 55
Atomic number
60
65
70
75
80
85
Figure 7.23 AES sensitivity factors normalized to the CuLMM line for 10 keV electron radiation. Sensitivity factors are calculated from the peak-to-peak heights in differential spectra.
(Reproduced with permission from Ref. [3]. © 2003 IM Publications.)
7.4.3
Composition Depth Profiling
We often need to characterize the changes in composition with distance from a
surface plane. XPS and AES can analyze such composition changes. The most
commonly used method to obtain a depth profile of composition is sputter depth
profiling using an ion gun. The ion gun provides a flux of positively charged argon
ions with a current density of 1–50 μA mm−2 and an energy of 0.5–5 keV. The ion
beam bombards a sample, causing it to eject atoms from the surface. A rastering
ion beam directed at a surface produces a crater. We can obtain a profile of the
near-surface compositions by examining the AES and XPS spectra of the crater
at its different depths. For example, Figure 7.24 shows an XPS depth profile of a
titanium surface coated with calcium phosphate. The depth scale in the profile is
not from a direct thickness measurement; instead, it is calculated from the etching
rate of the sample caused by ion beam bombardment. The etching rates depend
on the sputter yield, which is the number of atoms ejected by an ion. Sputter yield
data, unfortunately, are not commonly available and should be experimentally
determined. It is strongly suggested to calibrate the depth scale when the etching
rate is obtained from published data of sputter yields.
90
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
100
Atomic concentration (%)
90
80
C (1s)
O (1s)
P (2p)
Ca (2p)
Ti (2p)
70
60
50
40
30
20
10
0
−10
0
50
100
150
200
Thickness (nm)
Figure 7.24 XPS depth profile of a titanium surface coated with calcium phosphate which
contains Ca, P, and O. C in the profile is from surface contamination.
Quantitative analysis of a depth profile, in addition to quantifying concentrations,
needs to measure depth accurately. There are several factors we should be aware of
for resolution of depth measurement.
First, the etching rate for each type of atom is not constant even though the
ion beam energy and ion density are exactly the same. The consequence of
this phenomenon is that preferential etching occurs in samples containing
multiple elements. In samples comprising several elements that are not uniformly
distributed, certain areas will be etched faster than others because of preferential
etching. Thus, a rough crater surface is likely generated with increasing depth of
etching. The depth scale of the profile is based on the average etching rates. Thus,
the measured concentration of elements with higher etching rates (higher sputter
yield) will be higher than the real concentration.
Secondly, the incident ions can smear the interface in the depth profiles.
Figure 7.25 schematically illustrates interface smearing during depth profiling.
When an ion beam bombards a sample of a thin film that has a smooth interface
with a substrate, the depth profile of element A in the thin film often exhibits a
diffuse rather than a sharp interface profile, as should be the real case, as shown
on the lower part of Figure 7.25. This is also the case shown in Figure 7.24 in
which the smooth interface between the coating and titanium substrate becomes
diffuse in the profile. The main reason for interface smearing is that the incident
ions cause some coating atoms and/or substrate atoms to cross the interface. The
atom displacements caused by ion bombardment is not difficult to understand,
considering the energy brought into the sample atoms by the ions.
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248
A
B
A
B
Incident
Concentration
of A
ion
beam
Ideal profile
Measured profile
Figure 7.25 Smearing of the interface in a depth profile due to ion bombardment.
(Reproduced with permission from Ref. [6]. © 1991 Institute of Metals.)
Questions
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
Explain why H and He cannot be detected by Auger electron spectroscopy.
How many types of KLL Auger electrons are there? Rank them according to
their kinetic energies.
Why are the electron energies of OKLL and CKLL in Figure 7.3 different from
those in Figure 7.2? Estimate the work function of an aluminum oxide
surface from Figures 7.2 and 7.3.
Why are differential spectra preferred in AES analysis? Why are direct spectra
often used for quantitative analysis?
Why is ultrahigh vacuum necessary for an AES and XPS chamber?
Why are MgKα and AlKα used as X-ray sources for XPS? Do they excite 1s
photoelectron emission of metals such as Ti and Fe? If not, how do we detect
such elements?
What are two main functions of an ion gun in an AES and XPS system?
What are the differences between electron energy analyzers for AES and
XPS? Why?
In XPS, we need to detect energy shifts of 0.1 eV at energy levels up to 1500 eV.
For an energy analyzer with the energy resolution limit, ΔE/E = 5.3 × 10−3 ,
does a pass energy of 10 eV satisfy the requirement?
249
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7.4 Qualitative and Quantitative Analysis
7 Electron Spectroscopy for Surface Analysis
5000
C 1s
2
CF
5
4000
4
CF2
3
1
CF2
CH2
y
CF3
?
Counts
x
?
3000
2000
?
?
?
1000
X
0
0
295
290
Binding energy [eV]
285
Figure 7.26 An XPS spectrum showing carbon (1s) binding energies of a polymer sample.
(Reproduced with permission from Ref. [7]. © 1992 John Wiley & Sons Ltd.)
7.10 How can you tell Auger peaks from photoelectron peaks in an XPS spectrum?
7.11 The chemical shifts of binding energy are related to electronegativity (charge
on an atom). Using Figure 7.26, determine the chemical shifts of C 1s for a
polymer by identifying the binding energy peaks for different carbon atoms
in its chemical structure.
7.12 Figure 7.2 shows the O 1s peak is higher than the C 1s peak. Can you
conclude the specimen surface has a ratio of oxygen to carbon higher than
1 from the spectrum? Note that the XPS sensitivity factors of oxygen and
carbon are 0.66 and 0.25, respectively.
7.13 Composition maps may be obtained by EDS, AES and XPS techniques.
Please indicate the right technique(s) for each of the following types of
sample: thin film of oxides, polycrystalline metals, and nanometer-thick
coatings of metal on a polymer.
7.14 Compare AES and XPS with respect to the following aspects: energy source,
signals from the sample, detectable elements, spatial resolution and applicability to organic samples.
References
1. Watts, J.F. (1990) An Introduction
3. Briggs, D. and Grant, J.T. (2003) Surface
to Surface Analysis by Electron Spectroscopy, Oxford University Press,
Oxford.
2. Prutton, M. and El Gomati, M.M. (2006)
Scanning Auger Electron Microscopy, John
Wiley & Sons, Ltd, Chichester.
Analysis by Auger and X-Ray Photoelectron
Spectroscopy, IM Publications and Surface
Spectra Ltd, Chichester.
4. Briggs, D. and Seah, M.P. (1990) Practical
Surface Analysis, Vol. 1, John Wiley &
Sons, Ltd, Chichester.
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250
5. Vickerman, J.C. (1997) Surface Analysis:
Further Reading
The Principal Techniques, John Wiley &
Sons, Ltd, Chichester.
6. Smith, G.C. (1991) Quantitative Surface
Analysis for Materials Science, Institute of
Metals, London.
7. Beamson, G. and Griggs, D. (1992) High
Resolution XPS of Organic Polymers, John
Wiley & Sons, Ltd, Chichester.
Brandon, D. and Kaplan, W.D. (1999) Microstructural Characterization of Materials,
John Wiley & Sons, Ltd, Chichester.
Eberhart, J.P. (1991) Structural and Chemical
Analysis of Materials, John Wiley & Sons,
Ltd, Chichester.
251
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Further Reading
8
Secondary Ion Mass Spectrometry for Surface Analysis
Secondary ion mass spectrometry (SIMS) is a relatively new technique for surface
chemical analysis compared with Auger electron spectroscopy (AES) and X-ray
photoelectron spectroscopy (XPS). SIMS examines the mass of ions, instead of
energy of electrons, escaped from a solid surface to obtain information on surface
chemistry. The term ‘‘secondary ion’’ is used to distinguish ‘‘primary ion’’ that is
the energy source for knocking out ions from a solid surface. The advantages of
SIMS over electron spectroscopy are:
• detection of all the chemical elements in the periodic table, including hydrogen
that cannot be detected by the AES or XPS;
• detection of elements in concentrations as low as 10− 6 , while AES or XPS
detection limits are concentration levels of 0.1 at%;
• limitation of the detection to the top one or two atomic layers of a solid surface
(<1 nm); and
• distinguish between different isotopes of elements.
Such features make SIMS a powerful technique for surface analysis. However,
SIMS as a surface analysis technique has not yet reached a mature stage because
it is still under development in both theoretical and experimental aspects. This
lack of maturity is attributed to the complicated nature of secondary ion yield
from a solid surface. Complexity of ion yield means that SIMS is less likely to
be used for quantitative analysis because the intensity of secondary ions is not a
simple function of chemical concentrations at the solid surface. SIMS can be either
destructive or nondestructive to the surface being analyzed. The destructive type
is called dynamic SIMS; it is particularly useful for depth profiling in chemistry.
The nondestructive type is called static SIMS. Both types of SIMS instruments are
widely used for surface chemical examination.
8.1
Basic Principles
SIMS uses energized primary particles, usually ions such as Ar+ , Ga+ , and Cs+ , to
bombard a solid surface in order to induce sputtering of secondary particles from
an area, as illustrated in Figure 8.1. The interactions between primary ions and
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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253
8 Secondary Ion Mass Spectrometry for Surface Analysis
Secondary
particles
Primary
particle
Surface
region
Figure 8.1
Secondary particle generation by an energetic primary particle.
the solid are rather complicated. First, the secondary particles include electrons,
neutral species of atoms or molecules, and ions. The majority of the secondary
particles are neutral and not useful in SIMS. Only the secondary ions generated
by the bombarding process carry chemical information. Secondly, the interactions
are often more than a simply one-to-one knock-out of a surface ion by a primary
ion. Commonly, the primary ions induce a series of collisions (collision cascade) in
a solid because the energy of a primary ion is transferred by collisions between
atoms in a solid before secondary ions on the surface are emitted. The generation
of secondary ions involves sputtering and ionization, which are introduced in the
following section.
8.1.1
Secondary Ion Generation
Emission of secondary particles can result from collision sputtering or from other
processes such as thermal sputtering, which are illustrated in Figure 8.2. Collision
sputtering includes direct collision sputtering and slow collision sputtering. The former
can be considered as a direct impact between a primary ion and a surface atom as
illustrated in Figure 8.2a. Direct collision sputtering is extremely fast, and occurs in
the range of 10− 15 to 10− 14 s after the primary ion strikes a surface. Slow collision
sputtering, illustrated in Figure 8.2b, represents the case that a primary ion never
has chance to collide with a surface atom; instead, atoms in the solid transfer the
impact energy to surface atoms after a series of collisions. The timescale of slow
collision sputtering is in the range of 10− 14 to 10− 12 s. Thermal sputtering occurs
when the density of primary ions is high. It is a process of transient vaporization
of the surface area impacted by primary ions, as illustrated in Figure 8.2c. Thermal
sputtering is slower than collision sputtering, and occurs in the range of 10− 13 to
10− 10 s. Thermal sputtering not only includes thermal but also electronic excitation
when the solid has poor electronic conduction.
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254
(a)
(b)
(c)
Figure 8.2 The sputtering process in SIMS: (a) direct collision sputtering; (b) collision cascade; and (c) thermal sputtering. (Reproduced with kind permission of Springer Science
and Business Media from Ref. [1]. © 1981 Springer Science.)
Only a small portion of secondary particles (∼1% of total secondary particles)
are ionized and become the secondary ions that are analyzed in SIMS. A sputtered
particle faces competition between ionization and neutralization processes when
it escapes a sample surface. The ionization probability represents the chance of a
sputtered particle being an ion. The ionization probability is strongly affected by
the electronic properties of the sample matrix. Ionization directly affects the signal
intensity of secondary ions as shown in the basic equation of secondary ion yield.
Im Ip Ym α + θm η
(8.1)
The secondary ion current (Im ) of chemical species m is collectively determined by
the primary ion flux (Ip ), the sputter yield (Ym, number of secondary ions generated
by one primary ion), and the ionization probability. α + represents the probability
for positive ions, θ m is the fractional concentration of species m in the surface layer,
and η is the transmission of the detection system. The transmission is defined as the
ratio of the ions detected to ions emitted, and it varies from 0 to 1 depending on the
analyzer. The sensitivity of SIMS to element m is controlled by the factors Ym , α + ,
and η. Ym generally increases with beam energy and with the primary ion mass. It
also varies with the types of atomic bonding in target samples.
Under the same experimental conditions, the yield of elemental secondary ions
(being considered as a combined effect of Ym and α + ) can vary by several orders
of magnitude across the periodic table, as shown in Figure 8.3, that exhibits
255
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8.1 Basic Principles
8 Secondary Ion Mass Spectrometry for Surface Analysis
Ca
6
Mg
Be Al
B
Ti
Ru
Cr
Ga Mo
Mn
Zr
Si
Fe
Nb
In
Ba
V
Re
W
Hf
Co
5
Pd
Os
Ta
log / +rel
Ni
4
Th
Ge
P
Sn
Zn
H
Pb
Ir
Ag
Sb
As
C
O
3
Sb Cd
Hg
Pt
S
2
Bi
Te
Au
N
20
40
60
Atomic number
80
100
Figure 8.3 Variation of positive ion yield among chemical elements under bombardment of
13.5 keV O−1 . (o) indicates a pure element, () indicates a compound. (Reproduced with
permission from Ref. [2, Figure 3]. © 1977 American Chemical Society.)
the relative yield intensity among elements. Also, the secondary ion yield for a
particular element dramatically varies with chemical state, as shown in Table 8.1.
For example, the positive Al ion yield in its oxide state is 100 times higher than in
its pure state. Such effects are mainly attributed to the ionization process because
the sputter yield only varies by a factor of about 3–5 across the periodic table at a
given bombardment energy.
There is no simple method to determine the ionization probability because the
understanding of the ionization process is still limited. Ionization mechanisms
Table 8.1
Comparison of secondary ion yield in pure metals and their oxide.
Metal
Clean elements M+ yield
Oxide M+ yield
Al
Ti
Cr
Fe
Cu
Mo
Ba
W
Si
Ge
0.007
0.0013
0.0012
0.0015
0.0003
0.00065
0.0002
0.00009
0.0084
0.0044
0.7
0.4
1.2
0.35
0.007
0.4
0.03
0.035
0.58
0.02
Data reproduced with permission from Ref. [3]. © 1989 John Wiley & Sons Ltd.
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256
differ between materials. For metals, a departing atom may transfer its electrons
to the surface, while for ionic solids, secondary ions may form by breaking atomic
bonds. It is also likely that rapid electronic transitions in the surface region will
neutralize any ions before they can escape from the surface. Thus, ionization may
occur by fragmentation of secondary particles within a certain distance from the
surface. The fragmentation of a neutral particle may result from its high vibrational
motion because its internal energy increases in collision sputtering.
The important features of the sputter ionization process can be summarized as
follows. First, the point at which the secondary particles escape from the surface
is not the point of the initial impact by the primary ion. Instead, there is a surface
damage zone that includes the points of primary particle impact and secondary
particle escape. Secondly, the cascade collision results in generation of secondary
ions with much lower energy than that of primary ions. Thirdly, there is significant
variation in secondary ion yield with chemical elements and chemical states of the
surface, which makes quantitative analysis difficult.
8.1.2
Dynamic and Static SIMS
Sputtering is, fundamentally, a process of damaging a surface. The energetic
primary ions remove atoms, atom clusters, molecules, or molecular fragments
from the surface region of a sample. Thus, the chemical structures of the surface
may be destroyed during SIMS examination. This is especially true when the high
flux of primary ions bombards a surface. SIMS with high flux of primary ion
bombardment is referred to as dynamic SIMS. Dynamic SIMS is able to remove
many layers of atoms in the surface region and provide elemental distributions in
a depth profile, similar to AES and XPS.
In order to analyze surface chemical structures, static SIMS has been developed
in which a low flux of primary ions is used in order to avoid the possibility that any
surface area is bombarded by primary ions twice. To do so, the dose of primary ions
never exceeds 1013 ions cm−2 of surface area. We estimate the density of surface
atoms as about 1015 atoms cm−2 by assuming the area of each atom as about
0.1 nm2 . The low dose of primary ions used in static SIMS means that less than
1% of the surface atoms or molecules are bombarded. Figure 8.4 schematically
illustrates static SIMS. A primary ion bombardment only generates damage to a
zone with a cross section (σ ) less than 10 nm2 (= 10−13 cm2 ) on the surface. A
damaged surface area is defined as a region that includes the impact point of a
primary ion and escape point of a secondary ion. Thus, static SIMS is considered
as a nondestructive method for surface analysis. For static analysis, the integrity of
the surface should be maintained within the timescale of the SIMS process.
We can estimate the timescale in which the whole surface layer is affected
by the primary ions. The lifetime of a surface may be simply estimated from the
primary ion flux (Ip ) and damage cross section (σ ) generated by each impact. Ip
is commonly measured in A cm−2 (1 A = 6.2 × 1018 charged particles per second).
Assume that each primary ion generates σ = 10−13 cm2 . Then, 1013 primary ions
257
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8.1 Basic Principles
8 Secondary Ion Mass Spectrometry for Surface Analysis
a
σ
2d
c
b
a: surface layer
b: bulk
c: damaged zone
σ is cross-sectional area
2r
Figure 8.4 Static SIMS. Primary ion bombardment results in surface damage and
emission of ions and neutral atoms. The
damaged area is quantified by the damage
cross section (σ ). In static SIMS the total
primary ion dose should be limited so that
only small portion of the surface is damaged. (a) surface layer; (b) bulk; (c) damaged zone; (d) depth of damage zone; and
(r) radius of damage zone.
cm−2 will affect the whole surface area of 1 cm2 . This means that the lifetime of a
surface with the flux density Ip = 1 μA cm−2 (= 6.2 × 1012 ions cm−2 ) is less than
1 s. Apparently, 1 μA cm−2 of flux density for primary ions is too high for static
SIMS. Since it is commonly accepted for the static SIMS condition to limit the total
amount of primary ions up to 1013 ions cm−2 , for a 10-min duration of static SIMS
examination a primary flux density of about 2.7 nA cm−2 is required to preserve the
chemical structure of the surface top layer where the secondary ions are emitted.
This flux is extremely low compared with that of dynamic SIMS, which requires
a flux density of greater than 1 μA cm−2 to ensure a reasonable erosion rate of
surface for depth profiling.
8.2
Instrumentation
SIMS requires an ultrahigh vacuum environment, similar to AES and XPS. The
ultrahigh vacuum environment ensures that trajectories of ions remain undisturbed
during SIMS surface analysis. The SIMS vacuum chamber and pumping system
is not much different from that for AES and XPS. Figure 8.5 illustrates common
SIMS structure in a vacuum chamber in which there are two main components: a
primary ion system and a mass analyzer system. The primary ion system includes a
primary ion source, a Wien filter and ion-beam deflector. The mass analysis system
includes a secondary ion extractor filter, mass analyzer, and ion detector.
8.2.1
Primary Ion System
A system generating a primary ion beam consists of three main parts: ion source,
ion filter, and deflector, as schematically illustrated in Figure 8.5. The ion source
produces primary ions with a certain kinetic energy. The ion filter purifies the
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258
ors
x-y flect
de
Io
/ fil n ext
ter rac
tor
en
Wi e r
filt
M
an ass
aly
zer
Ion urce
so
Primary ion
system
Detector
Mass spectrum
Sample
Figure 8.5 SIMS instrumentation.
primary ions and rejects unwanted ions in the primary ion beam. The purified
ions are condensed to a focused beam using an electromagnetic lens. The deflector
makes the focused ion beam raster on the sample surface in two orthogonal
directions; its function is similar to the electron-beam deflector in the scanning
electron microscope (SEM).
8.2.1.1 Ion Sources
The commonly used primary ions include argon (Ar+ ), xenon (Xe+ ), oxygen (O2 + ),
gallium (Ga+ ), and cesium (Cs+ ) ions. Heavier metal ions such as bismuth (Bi+ ) are
also available in modern static SIMS instruments. The ions of elements normally
occurring in gaseous phases, such as oxygen and argon, are produced by electron
bombardment sources or plasma ion sources. Electron bombardment sources use a
circular filament cathode surrounding a cylindrical grid anode, as illustrated in
Figure 8.6. The gas to be ionized is injected into the open space of the grid, and
the gas molecules are bombarded by the electrons emitted from the cathode. The
electrons travel in orbits inside the grid in order to increase their chances of striking
gas molecules. An extraction field inducted in the grid will draw the gas ion beam
through an opening in the center of the extractor. The electron bombardment
sources provide moderate brightness of primary ions (∼105 A m−2 per solid angle).
Plasma ion sources can produce much higher ion beam brightness than the
electron bombardment source, up to 107 A m−2 per solid angle. Plasma sources use
a source gas at high pressure. The duoplasmatron source is a commonly used plasma
source, illustrated in Figure 8.7. It has a hollow cathode containing a high-pressure
source gas, an intermediate electrode, and an anode mounted along the axis of the
cathode hollow. The current between cathode and anode generates arcs between the
cathode and intermediate electrode, as well as between the intermediate electrode
and anode. The plasma beam will flow through a small aperture in the center
of the anode. A beam with high brightness is produced and is especially suited
for dynamic SIMS, which needs a high yield of secondary particles and high
259
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8.2 Instrumentation
8 Secondary Ion Mass Spectrometry for Surface Analysis
Grid
(+VE W.R.T. Filament)
Extractor
Filament
Gas
supply
Electrons orbit
through center
of cell
Repellor
(−VE W.R.T. Filament)
Figure 8.6 Electron-bombardment source. (Reproduced with permission from Ref. [4]. ©
2001 IM Publications.)
Cathode
Intermediate
electrode
Anode
Extractor
B
Gas
Plasma discharge
Figure 8.7 Duoplasmatron ion source. The magnetic field marked B intensifies the plasma
by confining electrons close to the axis. (Reproduced with permission from Ref. [4]. © 2001
IM Publications.)
erosion rates. The O2 + ion beam is commonly used because it can increase positive
secondary ion yield.
Liquid-metal ion sources are used for producing a Ga+ ion beam. The working
principles of a liquid-metal ion source are similar to a field emission gun for
electrons. A strong electrical field strips off electrons from the source liquid metal
to generate a metal ion flow from the fine tip of a needle. Gallium is a metal with
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260
a low melting temperature of 29.8 ◦ C, and hence it is suitable for this purpose.
In a liquid-metal ion source, liquid gallium is coated on a metal reservoir and a
needle is welded to a heater filament, as illustrated in Figure 8.8. The liquid metal
can flow over the needle tip and extend to form a cone (the Taylor cone) under
a high electric field between the tip and extractor. During operation, a dynamic
equilibrium between extraction force and surface tension is reached in the liquid
metal. A constant ion current will flow out of the tip area as small as 10 nm and
generate an ion beam with high current density. This type of source exhibits very
high brightness (∼1010 A m−2 per steradian solid angle) and high spatial resolution.
Liquid-metal ion sources are also used to produce other ion beams of heavy metals
with relatively low melting temperature, such as bismuth (271.3 ◦ C).
Surface ionization sources are commonly used for producing a Cs+ ion beam.
Surface ionization is produced in a vacuum by heating a source metal that is
adsorbed onto the surface of a metal with a high work function. The ionization of
source metal atoms is realized by transferring electrons from the adsorbed metal
to the substrate of the metal because the work function of the substrate is higher
than the ionization potential. Then, positive Cs+ ions can be extracted from the
metal substrate to form an ion beam. The Cs+ ion beam is particularly useful for
enhancing negative secondary ions. The Cs+ ion beam exhibits uniform kinetic
energy and reasonable spatial resolution.
Support leg &
electrical contact
Extractor
Insulating base
Heater
filament
Needle
Reservoir
Liquid metal
Ion emission
Needle
Taylor cone
Figure 8.8 Liquid-metal ion source. The primary ion beam is extracted from the Taylor
cone of liquid metal. (Reproduced with permission from Ref. [4]. © 2001 IM Publications.)
261
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8.2 Instrumentation
8 Secondary Ion Mass Spectrometry for Surface Analysis
8.2.1.2 Wien Filter
A primary ion beam for SIMS analysis should ideally contain ions with identical
mass. Under the same electric field for accelerating the primary ions, the time
for two ions to reach the sample will be different if their mass is different. Time
accuracy is extremely important in the most widely used form of static SIMS,
time-of-flight secondary ion mass spectrometry (ToF SIMS), in which primary ions are
emitted in a pulse length of about 10−9 s. The primary ion beam likely contains
ions with different mass such as isotopic ions and impurity ions. Thus, the primary
ion beam should be purified before bombarding the sample using mass filters.
The Wien filter is a simple device to filter ions according to their mass. Figure 8.9
illustrates the working principle of the Wien filter. The magnetic and electric fields
are mutually orthogonal. Also, these two fields generate forces lateral to an ion
current, which is perpendicular to both fields. The lateral forces generated from
magnetic and electric fields will cancel out when the velocity of ions reaches a
specific value (vs ). The velocity of ions is determined by their mass, because all the
primary ions from a source have same kinetic energy Ek = 12 mv2 . Thus, only ions
that have a specific mass (ms ) do not experience a lateral force and pass the filter.
8.2.2
Mass Analysis System
The mass analysis system collects and analyzes the ion masses to produce mass
spectra with the assistance of a computer. The extractor filter extracts secondary ions
from the surface, selects a mass range of ions to analyze, and eliminates scattered
primary ions from a mass spectrum. The mass analyzer separates secondary ions
according to their ratios of mass to electric charge, and these ratios are the basic
signals for SIMS analysis. The detector counts the numbers of ions each with
specific ratios of mass to electric charge. The mass analyzer, the critical component
Selection aperture
Heavy ions
Required beam ions
Light ions
− − −
− −
+
+ + +
+ +
Figure 8.9
Electrostatic
B
Force: +
Magnetic
The Wien filter for ion mass selection.
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262
for secondary ion mass analysis, can be one of the following types: magnetic sector
analyzer, quadrupole analyzer, and time-of-flight analyzer.
8.2.2.1 Magnetic Sector Analyzer
This analyzer was the oldest type used for mass spectroscopy. Figure 8.10 illustrates
the working principles of selecting ion masses using a magnetic field. Secondary
ions are accelerated by an extraction potential of 4 kV before entering a magnetic
field. The magnetic field in the magnetic sector will impose a field force in a
direction orthogonal to the direction in which the ions travel. The ions with a given
kinetic energy will change their travel path to a circular trajectory. The radius of
path curvature R has the following relationship with the ion mass
R=
(2V)1/2 m 1/2
B
z
(8.2)
where the extraction potential (V) is constant. We can adjust the magnetic field
strength (B), to select ions with a certain mass-to-charge ratio (m/z) with a fixed
radius of magnetic sector R. Thus, for given magnetic strength, only ions with
selected m/z can travel through the exit slit of the magnetic sector. A shortcoming
of the magnetic sector analyzer is that it can only analyze the secondary ions by
sequential selection of m/z. The magnetic sector analyzer is suitable for dynamic
SIMS experiments in which a few specific elemental ions are measured. The ability
to resolve the ion mass is limited by the kinetic energy variations in the ions
entering the sector. Secondary ions can obtain various amounts of kinetic energy
when they are ejected from a surface. The initial kinetic energy of secondary ions
may vary up to 100 eV for elemental ions. When taking this initial kinetic energy
into account in Eq. (8.2), we should replace V with V. Consequently, a value
of (m/z) will be selected with a given magnetic strength. The parameter, mass
resolution, is used to evaluate the quality of mass analyzers in SIMS. The mass
resolution is defined as the ratio of m/m. An electrostatic field is used to reduce
the kinetic-energy bandwidth of ions before entering the magnetic sector analyzer.
Input
slit
Region of uniform magnetic
field
Sample
Output slit
Detector
Figure 8.10 Magnetic sector analyzer. (Reproduced with permission from Ref. [5]. © 1991
Institute of Metals.)
263
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8.2 Instrumentation
8 Secondary Ion Mass Spectrometry for Surface Analysis
After kinetic-energy correction, the mass resolution of a magnetic sector analyzer
can reach a high 104 level.
8.2.2.2 Quadrupole Mass Analyzer
The quadrupole mass analyzer selects ions with a certain m/z by generating
unstable oscillation travels for the nonselected ions. Oscillations of ion trajectories
are created by an electric field combining a constant direct current (DC) and
alternating current with a radio frequency (RF). Figure 8.11 illustrates the working
principles of a quadrupole mass analyzer. The secondary ions are accelerated by
an extraction field, and then the ions travel through the center of four circular
rod electrodes. Combined DC and RF voltages are applied to one pair of rods and
equal but opposite combined voltages are applied to another pair of rods. Such an
arrangement of electric fields generates ion oscillation. The oscillation can be so
severe that ion trajectories become unstable and ions strike the rods. Ions with
unstable trajectories cannot travel through the exit slit of the analyzer to reach
the mass detector. Only the ions with a certain m/z have stable trajectories and
can pass through the exit slit under a given ratio of DC:AC voltages. The analyzer
is a sequential type that only allows the ions with single m/z values to reach the
detector. Thus, the quadrupole analyzer is a device with low transmission, as less
than 1% of ions can reach the detector at any time. To obtain a whole m/z spectrum,
the analyzer increases the voltages but keeps the ratio of DC:AC voltages constant.
8.2.2.3 Time-of-Flight Analyzer
The ToF analyzer is the most widely used analyzer in static SIMS. As its name
indicates, for this analyzer the flight time of an ion is the parameter for measurement. When ions are obtained with a constant kinetic energy from an acceleration
potential (V) of 3–8 kV, the flight time of ions through a distance (L) of flight tube
Low-voltage
ion
extraction
Sample
2r0
2r
Pre/postfilter
quadrupole
Detector
+
(a)
−
d.c. = U r.f. = Vcos ωt
(b)
Figure 8.11 A quadrupole analyzer. The oscillations of ions are generated by combined DC
and AC electric fields using four cylindrical rods: (a) travel path of secondary ions in the
analyzer and (b) electrode arrangement of the analyzer. (Reprinted by permission of Oxford
University Press from Ref. [6]. © 1989 Oxford University Press.)
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264
to reach a detector is calculated.
t = L(2V)−1/2
m 1/2
(8.3)
z
Thus, the m/z of ions is analyzed by measuring their flight time in the analyzer.
Heavier ions will have longer flight times in the tube. To measure the time of
flight, precisely pulsed primary ions should be used. The pulse is controlled by
a highly accurate clock. The pulse periods are typically of the order of 10 ns. The
flight time of ions to the detector is electronically measured and converted to m/z.
In a pulse period, all the ions can be measured and a whole mass spectrum can be
obtained almost simultaneously. Again, the initial kinetic energy of secondary ions
will affect the resolution of mass analysis, because the velocity could be different
when ions with the same m/z enter the flight tube. To overcome the problem of
resolution of flight time, the ToF analyzer is constructed in such way that the ions
will be reflected by a mirror, as illustrated in Figure 8.12. The mirror is composed
of a series of precisely spaced rings to which a gradually increasing electric field
is applied. Ions with higher kinetic energy will penetrate further into the mirror
before being reflected. Thus, ions with the same m/z will arrive at the detector at
the same time if the mirror has been tuned correctly.
Table 8.2 compares the main parameters of three mass analyzers. From Table 8.2
we can understand why the ToF analyzer has become so popular for static SIMS;
it provides high resolution, high transmission, and high sensitivity. The major
shortcoming of the ToF analyzer is its use of pulse primary ions. The ratio of
primary beam on- to off-time is only about 10−4 . Thus, it is not efficient for analysis
such as depth profiling of chemical elements.
Beam energy = 10 keV-target voltage
Collimating lens
± 3.5 kV
Extract
± 3.0 kV
Preamplifier
+
1st stage
20 M? between
each ring
1st stage
2.7 M? between
each ring
Grid
± 1.25 kV
Channel plate
detector
± 2.06 kV
Retard
± 3.09 kV
Retard
Gain = 2.3 kV
Output
Figure 8.12 Time-of-flight mass analyzer. The secondary ion beam is reflected by a mirror
to correct the flight time of ions with identical m/z. (Reproduced with permission from Ref.
[7]. © 1997 J.C. Vickerman.)
265
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8.2 Instrumentation
8 Secondary Ion Mass Spectrometry for Surface Analysis
Table 8.2
Comparison of SIMS mass analyzers.
Mass analyzer
Quadrupole
Magnetic sector
Time-of-flight
Mass
resolution
Range of mass
detection
Transmission
Manner of
detection
Relative
sensitivity
102 –103
104
>103
<103
>104
103 –104
0.01–0.1
0.1–0.5
0.5–1.0
Sequential
Sequential
Parallel
1
10
104
Data reproduced with permission from Ref. [7]. © 1997 John Wiley & Sons Ltd.
8.3
Surface Structure Analysis
Analysis of surface chemical structure requires use of the static SIMS technique to
ensure that the major portion of the surface should not be affected by secondary ion
emission. ToF SIMS is the most widely used static SIMS technique. As its name
indicates, ToF SIMS uses the ToF mass analyzer to measure m/z of secondary
ions. ToF SIMS is a standalone instrument, not incorporated into or attached to
other SIMS instruments as for dynamic SIMS. A typical structure is illustrated in
Figure 8.13.
8.3.1
Experimental Aspects
8.3.1.1 Primary Ions
The primary ions commonly used for ToF SIMS are heavy metals such as Ga+ ,
Cs+ , and Bi+ with atomic weights of 69.72, 132.91, and 208.98 amu (atomic mass
units), respectively. The high-mass ions increase the yield of secondary ions with
limited increase of the damaged cross section (σ ). The energy of the primary ion
beam can be varied from 1 to 25 keV. Higher energy may not be favorable because
it can cause excessive fragmentation and make SIMS spectra difficult to analyze.
Thus, ToF analysis is better with heavy primary ions ‘‘gently’’ striking a surface to
be analyzed.
8.3.1.2 Flood Gun
ToF SIMS instruments are equipped with an electron flood gun, as shown in
Figure 8.13. The flood gun solves the problem of surface charging of insulating
samples, similar to the surface-charging problem in electron spectroscopy. A sample
surface will be positively charged when bombarded by primary ions. The positive
primary ions will be implanted into the sample and also secondary electrons will
be ejected from the sample surface. The surface charge can rapidly build electric
potential on a surface up to several hundred volts. Such potential will increase
the kinetic energy of positive secondary ions emitted from surfaces; and on the
other hand, it will retard negative ion emission. Between two pulses of primary ion
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266
1
The sample
2
Primary ion gun
3
Flood gun
4
Mass analyzer
5
Ion detector
4
5
2
3
1
Figure 8.13 Time-of-flight SIMS instrumentation. (Reproduced with permission from
Ref. [4]. © 2001 IM Publications.)
beam bombardment, the flood gun provides electrons with relatively low energy
to irradiate the sample surface and make it electrically neutral or even negative.
Driving the surface potential down to negative is necessary to ensure release
of negative secondary ions. Thus, the higher flux (∼10 × higher) of low-energy
electrons from the flood gun will be used for examining the negative secondary
ions and fragments.
8.3.1.3 Sample Handling
The samples for ToF SIMS should be carefully handled to avoid chemical contamination and surface roughening. Because contamination can seriously distort the
ToF SIMS spectrum of a sample surface, surface roughness, and positioning in
the instrument are critical. Regular cleaning of the sample surface ensures that the
surface is free from contamination. ToF SIMS spectra are extremely sensitive to
the atoms and molecules nearby, no matter whether they are in the air (and hence
can be adsorbed) or whether they come from physically contacting other objects.
267
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8.3 Surface Structure Analysis
8 Secondary Ion Mass Spectrometry for Surface Analysis
A sample surface can even be contaminated by the plastic from a bag or box used
to store the sample. Organic compounds from such containers may be released
into the air and adsorbed on a cleaned sample surface. For inorganic samples, we
may clean the surface by sputtering away the contamination using primary ions
before acquiring secondary ions. Sputtering, however, is not suitable for organic
samples because it may destroy the structure of an organic surface. Certain solvents to which the sample is inert, such as hexane, may be used to rinse organic
surfaces.
Roughness or topographic features of a sample surface can cause a significant
reduction in mass resolution. The main reason for this is that the electrostatic field
on a rough surface is not even. The field strength is reduced in dips and troughs
from the uppermost surface. The mass resolution will be degraded significantly
when a surface has peak-to-trough roughness beyond 10 μm.
The positioning of the sample relative to the mass analyzer is also important.
Inaccuracy in the distance to the secondary ion extractor associated with the mass
analyzer affects mass resolution, but does not strongly affect spectral intensity.
Tilting the sample relative to the extractor causes more problems because tilting
will make the trajectories of the secondary ions curved when entering the mass
analyzer and will, as a result, distort the spectra. Large molecular fragments are
more affected by sample tilting. For example, a tilt angle of 4◦ will reduce the
relative spectral intensity of C7 H7 in polymer molecules by a factor of 2, but will
have little effect on the spectral intensity of CH3 .
8.3.2
Spectrum Interpretation
The secondary ion mass spectra expresses the detected intensities of secondary ions
versus their mass-to-charge ratio (m/z) where mass is in atomic mass unit (amu).
Figures 8.14–8.16 show examples of mass spectra produced using ToF SIMS. We
can identify individual ions, ion clusters, and molecular fragments according to
their m/z values. Two particular features of SIMS spectra are revealed in Figures
8.14–8.16. First, the spectrum can be either that of positive ions or negative ions.
For example, both Figures 8.14 and 8.15 are the mass spectra of polystyrene, but
Figure 8.14 is of positive ions, while Figure 8.15 is of negative ions. Secondly,
SIMS spectra appear more complicated than those of AES and XPS because there
are more peaks than the basic ion components. A SIMS spectrum often exhibits
secondary ions that are various combinations of atoms and ion fragments ejected
from the sample. For example, the spectrum of a simple inorganic compound,
NaNO3 , includes not only peaks of the ions that comprise the molecule, but also
peaks of adduct (unbonded associations of molecules) ions with high m/z values
including NaNO3 ·O− and NaNO3 ·NO− , as shown in Figure 8.16. The mass spectra
of polymers are even more complicated, as shown in the example of polystyrene
in Figure 8.14. Interpreting SIMS spectra, particularly those of polymers, requires
experience, and knowledge of materials.
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268
× 104
7
+
(C7 H7+) 91
6
Counts
5
4
3
+ (C6 H5+)
2
77
1
0
0
10
20
30
40
50
m/z
60
70
80
90
100
CH2 = C+
(C8 H7+)
Counts
15000
10000
+ (C9 H7+)
115
(C13 H9+)
+
103
+
(C10 H8+)
+
128
5000
(C12 H8+)
+
(C14 H10+)
165
178
152
0
100
110
120
130
140
150
m/z
160
170
180
190
200
Figure 8.14 Positive-ion ToF SIMS spectrum of polystyrene. (Reproduced with permission
from Ref. [8]. © 1998 Cambridge University Press.)
8.3.2.1 Element Identification
Identifying elements from a SIMS spectrum is relatively simple. The elements
can either be identified by their exact m/z or by detecting expected isotopes. To
obtain accurate mass measurement, the mass correlation with flight time should be
calibrated based on Eq. (8.3). The calibration can be done using a known ion mass
in the sample. There are general rules that are helpful for element identification,
given as follows. The great majority of metals give exclusively positive ions in static
SIMS conditions. The most electropositive elements, such as alkali and alkali-earth
metals, give intense positive ion peaks. The most electronegative elements, such
as O, F, Cl, Br, and I give intense negative ion peaks. Hydrogen gives a high yield
of both H+ and H− ions. The CH− peak is commonly more intense than the C−
peak. N is not usually detectable by an elemental peak. P is usually detected from
peaks of PO2 − and PO3 − .
A polymer surface commonly generates a complicated spectrum. The polymer
spectrum can be divided into three regions: submonomer, n-mer, and oligomer
regions. The submonomer region is the region where mass values are less than the
269
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8.3 Surface Structure Analysis
8 Secondary Ion Mass Spectrometry for Surface Analysis
× 104
18
16
14
Counts
12
10
× 10
8
6
60
70
80
90
60
70
80
90
4
2
0
0
10
20
30
40
50
m/z
100
Figure 8.15 Negative-ion ToF SIMS spectrum of polystyrene. (Reproduced with permission
from Ref. [8]. © 1998 Cambridge University Press.)
O−
H−
Intensity
× 104
3.0
2.5
2.0
1.5
1.0
OH−
NO−
NO2−
20
Intensity
×
40
Mass
−
103
NO3
1.5
1.0
0.5
60
80
× 10
2.0
1.5
1.0 NaNO •O− NaNO •NO−
3
3
0.5
Intensity
110
120
Mass
NaNO3•NO3−
2
NaNO3•NO2−
130
140
Mass
Figure 8.16 Negative ToF spectrum of NaNO3 . (Reproduced with permission from Ref. [4].
© 2001 IM Publications.)
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270
monomer mass. This is the main region of spectra to examine when identifying
polymer molecules because it provides information on the basic chemical information of polymers. For example, the monomer mass of polystyrene is 104 amu. The
spectral region at m/z < 104 in Figure 8.14 provides basic structural information
on polystyrene. The negative-ion spectrum of a polymer is simpler than that of its
positive-ion spectrum, as can be seen by comparing Figure 8.15 with Figure 8.14.
The positive-ion spectrum frequently includes hydrocarbon-originating ions, which
do not provide much structure information for the polymer.
The n-mer region of a spectrum includes a small number of monomer units or
monomer units plus fragments. This region may contain more information on the
macromolecular structure. This region is more important for polymers containing
more than one type of monomer (copolymers). Also, the region can reveal the state
of crosslinking in polymers. The oligomer region is at high m/z, in which peaks
are generated by a process called cationization. Cationization is the laying down of
a thin layer of organic substance or polymer on a silver substrate. ToF SIMS is able
to detect the peaks of organic molecules (M) attached to Ag as [Mx + Ag]+ . The peaks
of cationization can reach m/z levels at a scale of 103 . Figure 8.17 shows an example
of cationization used to examine an organic residue on glass. The organic residue
was deposited on a clean silver substrate by rubbing glass over the substrate. The
monolayer of organic residue was sputtered with Ag. The oligomer region, in
principle, can be used for estimating the average molecular weight distribution of
polymeric materials.
The interpretation of polymer spectra has been the subject of extensive study;
thus, published sources are available to help with interpretation. Databases of ToF
× 104
420+ Ag
2.5
Intensity
2.0
1.5
140 u
1.0
140 u
0.5
140 u
140 u
500
600
700
800
900
1000
1100
mass/u
Figure 8.17 Positive ToF SIMS spectrum of a polymeric substance that has a repeat unit
of C10 H20 . (Reproduced with permission from Ref. [4]. © 2001 IM Publications.)
271
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8.3 Surface Structure Analysis
8 Secondary Ion Mass Spectrometry for Surface Analysis
× 104
6
Counts
5
4
3
2
Cs
1
0
0
20
40
60
80
100
120
140
160
180
200
m/z
Figure 8.18 Positive ToF SIMS spectrum of high-density polyethylene (HDPE). (Reproduced
with permission from Ref. [4]. © 2001 IM Publications.)
SIMS spectra have been established in which more than a thousand spectra for
surface analysis can be found. On the other hand, a regular cluster pattern of
hydrocarbon polymers is possibly used to interpret some polymer spectra. The
pattern is especially helpful when the standard spectra of samples to be analyzed
are not available. For example, the high-density polyethylene (HDPE) spectrum in
Figure 8.18 shows a cluster pattern. There are several clusters of peaks and each of
them represents a Cn Hm + (m = 0,. . ., 2n + 1) cluster in the positive ion spectrum
of HDPE. We can easily assign the clusters as C1 , C2 , C3, . . . because the mass of
each carbon atom is 12 amu. The peaks in each cluster represent the ions with the
same number of carbon ions but variation in hydrogen ions.
Generally, the intensity of ion peaks decreases with increasing ion mass. For
hydrocarbon polymers containing cyclic ions (aromatic hydrocarbon polymers)
such as polystyrene, which contains benzene rings, the Cn Hm + clusters in spectra
extend to the high-mass region. The characteristic peaks of such polymers are for
C7 H7 + and C6 H5 + clusters, which represent the cyclic ions with seven carbon
atoms and six carbon atoms, respectively. Table 8.3 lists a few characteristic
ion masses that are frequently encountered in surface analysis of polymeric
materials.
8.4
SIMS Imaging
SIMS instrumentation enables us to operate SIMS in a scanning mode because it
is equipped with an X–Y deflector on the primary ion beam. In scanning mode,
a focused primary ion beam scans over a surface area of the sample. Secondary
ions emitted in each pixel generate a two-dimensional SIMS image that reveals the
distributions of ions on a surface. Formation of SIMS images is quite similar to
chemical element mapping by energy dispersive spectroscopy (EDS) and AES.
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272
C9H19
CH3
n
n
CH2OH
(C6 H5 O)3 P–O
CH2OCOC17H35
CHOH
O(CH2CH2O)n H
C O C8 H17
O
O
C O C8 H17
CH CH2 O n
C17 H35 COOH
C15 H31 COOH
C17 H35 CONH2
C17 H33 CONH2
C21 H41 CONH2
(CH2 NHCOC17 H35 )2
CH3
CH2 CH2 O
Si O
CH3
77, 251, 327
267, 341, 359
63, 79, 93, 249, 325
71, 283
133, 219
121
149, 167, 261, 279
247, 419/435, 463/479, and so on
283
255
42, 282
42, 280
42, 336
42
57, 75, 113, 133
61, 105, 149
267, 285
239, 257
284
282
338
282, 310
59, 117, 175, 233
45, 89, 133, 177
59, 60, 75, 119, 149, 223
Characteristic secondary ions (m/z)
Negative
73, 147, 201, 221, 281
Positive
273
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Data reproduced with permission from Ref. [8]. © 1998 Cambridge University Press.
Triphenyl phosphate
Glyceryl monostearate
Nonyl phenol ethoxylate
Di-octyl phthalate
Stearic acid
Palmitic acid
Stearamide
Oleamide
Erucamide
Ethylene bis-stearamide
Poly(propylene glycol)
Poly(ethylene glycol)
Structure
Characteristic secondary ions and nominal mass of some molecules frequently encountered in polymer surfaces.
Poly(dimethyl-siloxane) (silicone)
Molecule
Table 8.3
8.4 SIMS Imaging
8 Secondary Ion Mass Spectrometry for Surface Analysis
8.4.1
Generation of SIMS Images
The liquid-metal ion sources of ToF SIMS can provide a focused ion beam with
a diameter of the order of 10−9 and 10−6 and even less, because the structure
of such a primary ion source is similar to the electron field emission gun in
electron microscopes. Gaseous ion sources used in dynamic SIMS can also provide
a focused primary ion beam for scanning. The commonly used diameters of ion
beams for scanning images are about 200 nm to 1 μm. The X–Y deflector attached
to the primary ion source rasters the beam on the sample surface. Each pixel
composing a SIMS image may comprise signals from a single selected m/z or a
few m/z in dynamic SIMS, as well as from a whole mass spectrum in ToF SIMS.
Figure 8.19 shows an example of a SIMS image of a cross section of a coating
on a titanium substrate. Images of positive ions in Figure 8.19 reveal the chemical
gradient in the coating composed of calcium phosphate. The images of Ca and Ti
ions clearly reveal the interface between the calcium phosphate coating and the
titanium substrate. The images of O and OH ions indicate that there is deficiency of
O2 and OH in the coating region near the interface because of lower ion intensities
there.
Ca
102
Ti
0
O
20 μm
141
0
61
0
OH
78
0
Figure 8.19 SIMS images of ceramic coating on titanium obtained with scanning ToF
SIMS. Ga+ primary ion beam generates the positive-ion images of Ca, Ti, O, and OH.
Chemical gradients of O and OH in the coating layer (left-hand sides of images) are
revealed.
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274
8.4.2
Image Quality
Ideally, we wish to obtain SIMS images with high spatial resolution of secondary
ion signals with high signal-to-noise ratios. However, reduction of pixel size causes
a decreasing number of secondary ions in each pixel. Smaller pixel size means
fewer atoms or molecules will be available to emit secondary ions in each pixel. This
situation is especially true for ToF SIMS imaging. ToF SIMS limits the primary
ion density to 1013 cm−2 . The number of primary ions in each pixel could be too
small to generate sufficient secondary ions. The signal-to-noise ratio for SIMS
imaging relies on counts of secondary ions received by a detector. To understand
the problem, we can estimate the counts of secondary ions in each pixel by the
ToF SIMS detector. Assuming a sputtering yield of 1, ionization probability of 10−3
and transmission of 0.5, we can only have about 50 secondary ions in each pixel of
1 μm2 based on Eq. (8.1). For molecular fragment ions, the signals are even weaker
because of their low sputtering yield.
One solution to the problem is to increase the ionization probability. This can be
done by choosing primary ions with heavy mass, for example, Bi+ or even C60 + ,
which contains 60 carbon atoms. The noise level can also be reduced by techniques
of digital image processing. For example, a fast Fourier transform technique has
been used to remove noise from the image. This technique transforms an image
from a space domain to a reciprocal domain by sine and cosine functions. Noise can
be readily filtered out in such domain. After a reverse Fourier transform, filtered
data produces an image with much less noise.
SIMS imaging can also be affected by surface topographic features. Particularly,
for insulating samples, the electron field intensity varies with surface height.
Correspondingly, the signals from secondary ions will vary even when there is no
chemical variation. We should be aware of this possible artifact when interpreting
SIMS. Thus, to reduce this misleading variation, the sample for SIMS imaging
should be as flat as possible. We may also check whether there is a topographic
effect by comparing SIMS images for several types of secondary ions. For example,
comparison of images of Ca and O ions in Figure 8.19 tells us that the oxygen
gradient in the coating is real, not an artifact of surface topography. Note the
contrast change near the interface region in the image of the O ions. This same
contrast change would appear in the image of Ca ions if the contrast had resulted
from the surface topography.
8.5
SIMS Depth Profiling
Early applications of SIMS were not for surface analysis, but for detecting trace
elements in near-surface regions of samples. The high sensitivity of SIMS to all
chemical elements enables us to trace any element with a concentration down
to subparts per million (ppm) levels. This is the main advantage of SIMS depth
275
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8.5 SIMS Depth Profiling
8 Secondary Ion Mass Spectrometry for Surface Analysis
profiling of trace elements with extremely low concentrations, compared with AES
and XPS depth profiling. SIMS depth profiling relies on primary ions removing
various elements from surface layers at a uniform sputtering rate. A steady state of
sputtering can be achieved after a certain time, even though various elements show
different sputtering rates initially. Depth profiling can be conducted in both dynamic
and static SIMS. Depth profiling by ToF SIMS is less efficient than by dynamic
SIMS because in ToF SIMS separated ion beams are used for etching and analysis
purposes. A depth profile is obtained by periodically switching between etching and
analysis. In addition, the pulse mode operation in ToF SIMS further slows down
the process. ToF SIMS, however, can be used to obtain more accurate depth profiles
if time is not a concern. The next section introduces depth profiling based on the
dynamic SIMS technique, which is very popular in analyzing electronic materials.
8.5.1
Generation of Depth Profiles
Depth profiling requires a focused ion beam rastering over a rectangular area,
similar to SIMS imaging. The area of depth profiles is usually in the range of
10 μm × 10 μm to 500 μm × 500 μm. The beam energy is in the range 1–20 keV,
and beam density is at the level of 1 μA cm−2 . An O2 + ion beam is commonly used
for positive-ion profiles. The oxygen ions generate an oxide layer, and such a layer
produces very high positive ion yields of electropositive elements. Cesium ions, Cs+ ,
are widely used for generating high negative-ion yields of the elements that exhibit
low positive-ion yields. The most widely used mass analyzer in dynamic SIMS is
the magnetic sector analyzer. The high mass resolution and good transmission
make the magnetic sector analyzer the top choice for depth profiling. However,
the quadrupole analyzer is used when shallow profiles are needed, as these require
only a low-energy primary beam and a low incident angle.
Figure 8.20 shows an example of a depth profile obtained by dynamic SIMS; it
reveals GaAs and Si layers coating an Al2 O3 substrate. In a SIMS depth profile, the
atomic density, or secondary ion intensity of elements being analyzed is plotted
against either depth (z) or sputtering time (t), and can be easily converted to
depth at a constant sputtering rate. The depth profile shown in Figure 8.20 clearly
indicates the location of GaAs/Si and Si/Al2 O3 interfaces. In Figure 8.20, the Ga
and As intensities do not drop to zero in the Si layer, even through such elements
do not exist there. Instead, there is background with intensity fluctuation of the
order of 1016 –1017 atoms cm−3 in the profile. This background level represents the
detection limit of the depth profile, that is, the lowest atom concentration of Ga
and As that can be detected.
8.5.2
Optimization of Depth Profiling
The best depth profiling detects extremely low concentrations of trace elements and
their accurate depth positions. Thus, for depth profiling of elements, high detection
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276
1024
107
GaAs/Si/Al2O3
O2+ primary beam
106
1022
+
Si
Ga2+
105
50%
1021
104
Si+
1020
As+
1019
103
Ga
Si+
102
1018
101
1017
1016
As+, Ga2+ secondary ion intensity (counts)
50%
Arsenic, silicon atom density (atoms/cm3)
Al2O3
Si
GaAs
1023
0
2
4
6
Depth (μm)
8
100
10
Figure 8.20 SIMS depth profile of the GaAs–Si–Al2 O3 system. (Reproduced with permission from Ref. [9]. © 1989 John Wiley & Sons.)
sensitivity, low detection limit, and high depth resolution are required. Detection
sensitivity is the ability to detect a given element in a sample. The detection limit
is referred to as the lowest atom concentration of a given element that can be
detected in a sample. The detection limit is determined by the level of background
signals. The ratio of peak intensity of a given element to the background intensity
(called the dynamic range) is often used to describe the quality of depth profiling. A
good dynamic range means high detection sensitivity and low detection limit. The
depth resolution is referred to as the accuracy of depth measurement for elemental
concentrations. It is commonly defined as a depth range (z or t) in which the
concentration (or secondary ion intensity) varies from 84.13 to 15.87% at a depth
profile with a step-like chemical gradient, as illustrated in Figure 8.21. Limitations
in depth resolution will distort the profile at the interface from truly step-like to a
gradual profile.
277
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8.5 SIMS Depth Profiling
8 Secondary Ion Mass Spectrometry for Surface Analysis
True concentration
100
Intensity/(t )
concentration C (z )%
Measured
concentration
50
Error function
d/(t)/dt
dC(z)/dz
84.13%
60.67%
−σ
+σ
Δt
Δz
15.87%
Sputter time t
depth z
Figure 8.21 Definition of depth resolution and its effect on depth profiling. (Reproduced
with permission from Ref. [7]. © 1997 John Wiley & Sons Ltd.)
Optimization of depth profiling relies on selection of proper experimental
conditions. The effects of processing parameters on the quality of profiles, including
primary beam energy, incident angle of primary beam and the analysis area versus
the sputtering area on a sample surface, are briefly introduced in the following
section.
8.5.2.1 Primary Beam Energy
The beam energy affects the depth resolution and sputtering yield. Higher beam
energy results in higher sputtering yield. However, a high-energy ion beam can
mobilize atoms in a sample, causing some atoms to move deeper into the sample
while causing some atoms to move toward the surface. Consequently, a highenergy primary ion beam induces a mixing of atoms and distorts the depth profile.
Figure 8.22 shows the effect of beam energy on depth resolution due to mixing,
as As doping atoms in the SiO2 are pushed into the Si by the high-energy beam.
Thus, lower beam energy is desirable to obtain better depth resolution.
8.5.2.2 Incident Angle of Primary Beam
The incident angle of the primary beam affects sputtering yield, ionization probability, and depth resolution. Generally, the sputtering yield decreases with increasing
incident angle and reaches a minimum at an angle normal to the surface. For
example, a Si sputtering yield under O2 + beam with the incident angle of 30◦ is 10
times higher than that of 90◦ . However, the ionization probability increases with
the incident angle and reaches a maximum at the angle normal to the surface. For
example, the ionization probability of Si under an O2 + beam with a incident angle
of 60◦ is 2 orders of magnitude higher than that of 30◦ . The high incident angle
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278
104
75As →SIO2,
8 keV, 5 × 1014cm−2
Normalized secondary ion intensity
103
102
11 keV O2
101
7 keV O2
4 keV O2
1.45 keV O2
100
0
15
30
45
Depth (nm)
60
75
90
Figure 8.22 Primary O2 + beam energy effects on depth profile of As doped in SiO2 substrate. (Reproduced with permission from Ref. [9]. © 1989 John Wiley & Sons.)
may also affect the depth resolution because of surface roughening by the primary
beam. The intensity inside a primary ion beam is not uniform but a Gaussian
distribution as the center of the beam has higher intensity than the edge. Such a
Gaussian distribution of ion intensity inside the beam generates uneven sputtering
when the beam rasters on the surface. The roughening by a beam normal to the
surface is more severe than by a beam with small incident angle. Surface roughness
will degrade the depth resolution. Thus, an optimized incident angle should be
decided by the purpose of depth profiling.
8.5.2.3 Analysis Area
The primary ion beam etches a well-defined crater in a sample by a beam deflector
as illustrated in Figure 8.23. Ideally, only the secondary ions emitted from the
crater bottom should be collected for depth profiling. However, secondary ions
will be collected at the same time as when the primary ions etch the crater. Thus,
the secondary ions from the crater walls may also contribute to the secondary
ions in analysis. Such secondary ions from crater walls do not represent the
279
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8.5 SIMS Depth Profiling
8 Secondary Ion Mass Spectrometry for Surface Analysis
Secondary ion intensity of layer species
105
Primary ion
beam
104
Surface
Layer
Detected region
Uniform penetration
103
Detected region over whole crater
102
Detected region within uniform
penetration region
101
100
0
1
2
3
4
Time or depth (arbitrary units)
Figure 8.23 Schematic illustrating the importance of selecting an analysis area smaller
than the crater bottom. (Reproduced with permission from Ref. [9]. © 1989 John Wiley &
Sons.)
true concentrations of elements at the crater bottom. To avoid this problem, the
analysis area should be smaller than the size of the crater. Thus, the profile will
not be affected by the crater walls, as illustrated in Figure 8.23. Commonly, an
electronic gate is incorporated in the detection system. The electronic gate will
switch off detection when the primary beam does not strike the analysis area in the
middle of the crater bottom. The electronic gate and proper optical arrangement
can significantly lower the detection limit to the order of 1016 atom cm3 , which is
equivalent to about 0.2 ppm.
Questions
8.1
8.2
8.3
8.4
Figure 8.24 shows the sputtering yield of copper atoms as a function of
bombarding energy from three types of primary ions: He, Ar, and Xe.
Determine which legend of the experimental data is for He, Ar, and Xe,
respectively; justify your decision.
Compare Figure 8.3 and the periodic table of the elements. Does the
comparison show the evidence that the ionization is the dominant factor for
the secondary ion yield?
Why is O2 + commonly used as the source of primary ions for dynamic SIMS
analysis?
What are the main differences between dynamic and static SIMS?
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280
102
101
Yield
100
Experimental
10−1
Theoretical
10−2
10−3
0.01
0.1
1
10
100
1000
10 000
Energy (keV)
Figure 8.24 Sputtering yield data of copper atoms as a function of primary-ion energy for
different primary ions. (Reproduced with permission from Ref. [7]. © 1997 John Wiley &
Sons Ltd.)
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
We may estimate the lifetime of a surface monolayer by assuming that each
primary ion will knock out one atom in the monolayer. Estimate the lifetime
of a surface monolayer bombarded by primary ion beam densities of 10 and
0.1 nA cm−2 , respectively. Why should the primary ion dose be even less
than that based on the lifetime estimation?
The positive-ion spectrum of TiO2 exhibits peaks at 48, 49, 64, and 65 m/z.
Try to assign the ions or ion clusters to those peaks.
Try to determine the ions in the negative SIMS spectrum of polystyrene in
Figure 8.15.
Identify ions in the cluster around 40 (m/z) in Figure 8.18.
Surface charging affects the analysis in EDS, XPS, and SIMS. What are the
similarities and differences for problems of surface charge among those
techniques?
Why does ToF SIMS use a pulsed, not continuous, primary ion beam?
Which type of primary ion source can provide better static SIMS analysis?
Why do we not recommend using the smallest diameter of a primary beam
for ToF SIMS imaging?
Can you determine the interdiffusion distances of atom A and B at their
interface region in a SIMS depth profile? Why?
Estimate the detection limit in term of the planer concentration shown in
the depth profile of Figure 8.20.
281
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8.5 SIMS Depth Profiling
8 Secondary Ion Mass Spectrometry for Surface Analysis
References
1. Behrisch, R. (ed.) (1981) Sputtering by
2.
3.
4.
5.
Particle Bombardment I, Springer-Verlag
Gmbh, Berlin.
Storms, H.A., Brown, K.F., and Stein,
J.D. (1977) Anal. Chem., 49(13), 2025.
Briggs, D., Brown, A., and Vickerman,
J.C. (1989) Handbook of Static Secondary
Ion Mass Spectrometry, John Wiley &
Sons, Ltd, Chichester.
Vickerman, J.C. and Briggs, D. (2001)
ToF-SIMS Surface Analysis by Mass Spectrometry, IM Publications and Surface
Spectra, Chichester and Manchester.
Smith, G.C. (1991) Quantitative Surface Analysis for Materials Science, The
Institute of Metals, London.
6. Vickerman, J.C., Brown, A., and Reed,
N.M. (1989) Secondary Ion Mass Spectrometry: Principles and Applications, Clarendon
Press, Oxford.
7. Vickerman, J.C. (1997) Surface Analysis:
The Principal Techniques, John Wiley &
Sons, Ltd, Chichester.
8. Briggs, D. (1998) Surface Analysis of Polymer by XPS and Static SIMS, Cambridge
University Press, Cambridge.
9. Wilson, R.G., Stevie, F.A., and Magee,
C.W. (1989) Secondary Ion Mass Spectrometry, a Practical Handbook for Depth
Profiling and Bulk Impurity Analysis, John
Wiley & Sons, Inc., New York.
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282
9
Vibrational Spectroscopy for Molecular Analysis
Vibrational spectroscopy is a technique to analyze the structure of molecules by examining the interaction between electromagnetic radiation and nuclear vibrations
in molecules. Vibrational spectroscopy is significantly different from the spectroscopic methods using interactions between materials and X-rays introduced in
Chapters 6 and 7. Vibrational spectroscopy uses electromagnetic waves with much
longer wavelengths, in the order of 10− 7 m, than the X-rays that are also electromagnetic waves but with wavelengths in the order of 10− 10 m. Typical electromagnetic
waves in vibrational spectroscopy are infrared light. Energies of infrared light
match with vibrational energies of molecules. Vibrational spectroscopy detects the
molecular vibrations by the absorption of infrared light or by the inelastic scattering
of light by a molecule. Vibrational spectroscopy can be used to examine gases, liquids, and solids. It is widely used to examine both inorganic and organic materials.
However, it cannot be used to examine metallic materials because they strongly
reflect electromagnetic waves. This chapter introduces two spectroscopic methods:
Fourier transform infrared spectroscopy (FTIR) and Raman microscopy (also called
micro-Raman), which are the vibrational spectroscopy techniques most commonly
used by scientists and engineers for materials characterization.
9.1
Theoretical Background
9.1.1
Electromagnetic Radiation
It is necessary to review electromagnetic radiation in general before discussing
its interaction with molecular vibrations. Electromagnetic radiation, traveling at
a constant speed of light, varies in wavelength over 10 orders of magnitude and
includes radio waves (∼102 m) to γ -rays (∼10−12 m) as illustrated in Figure 9.1.
Visible light occupies only a short range of wavelengths (0.40–0.75 × 10−6 m). The
energies of molecular vibrations match with those of electromagnetic radiation in
a wavelength range near visible light. The electromagnetic radiation in near visible
light is able to change the status of molecular vibrations and produce vibrational
spectra of molecules. Vibrational spectroscopy characterizes the electromagnetic
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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283
9 Vibrational Spectroscopy for Molecular Analysis
waves in terms of wave number (ν), which is defined as the reciprocal of wavelength
in the units of cm−1 .
ν=
1
λ
(9.1)
Thus, the wave number is the number of waves in a 1 cm-long wavetrain. It is
convenient for us to remember that wave number is proportional to the frequency
of the electromagnetic wave (ν) with a constant factor that is the reciprocal of the
speed of light (c).
ν=
1
ν
c
(9.2)
The wave number represents radiation energy, as does wavelength. As we know,
electromagnetic waves can be considered as photons. The photon energy is related
to the photon frequency (ν ph )
E = hνph
(9.3)
h is Planck’s constant (6.626 × 10−34 J s). Thus, the photon energy can be represented as its wave number.
E = hcv
(9.4)
The conversion constant (hc) is about 2.0 × 10−23 J cm. For a wave number of
1000 cm−1 , the corresponding energy should be only about 2.0 × 10−20 J or 0.12 eV.
Note that this is much smaller than the photon energy of X-rays, which is of the
order of 10 000 eV. As shown in Figure 9.1, the vibrational spectra are in the
wave number range from several hundreds to thousands. This indicates that the
vibrational energy of molecules are only in the order of about 10−2 –10−1 eV.
Energy E
10−4
6
Frequency ν´ 10
2
Wavelength λ 10
10−2
108
100
102
1010
10−2
104
1012
106
1014
10−4
1016
10−6
10−8
108
1010
1018
10−10
1020
Short
waves
Micro- Infrared
waves radiation
Vibrational
spectra
Ultraviolet
radiation
X-rays
Visible
Light
J/mol
Hz
10−12 m
cm−1
100 101 102 103 104
Wavenumber ν
Radio
waves
100
γ-rays
Figure 9.1 Energy, frequency, wavelength, and wave number ranges of electromagnetic
waves. Frequency range of molecular vibrations is in the infrared region close to visible
light. (Reproduced from Ref. [1].)
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284
9.1.2
Origin of Molecular Vibrations
Molecules in solids are always in vibration at their equilibrium positions, except at
the temperature of absolute zero (−273.15 ◦ C). Molecular vibrations can be simply
modeled as massless springs connecting nuclei in a molecule. Figure 9.2 illustrates
the simplest model of molecular vibrations: a diatomic molecule vibration by
stretching or compressing the bond (a massless spring) between two nuclei. The
vibrational energy can be calculated using the spring model. The force (F) due to
linear elastic deformation of the bond is proportional to displacement of two nuclei
from its equilibrium distance r e .
F = −Kr = −K(r − re )
(9.5)
The force constant K is a measure of bond strength and r is the distance between
two nuclei after displacement. Such vibration motion is considered as harmonic.
The potential energy of a harmonic vibration is expressed as E vib .
1
1
(9.6)
K(r)2 = K(r − re )2
2
2
Figure 9.3 illustrates the potential energy of harmonic motion as a parabolic function of displacement from the equilibrium position of nuclei. The harmonic curve
differs from a real relationship between energy and displacement in molecules.
Evib =
Center of gravity
Equilbrium
position
m1
Bond
m2
re
Maximum
displacement
position
rmax
Minimum
displacement
position
rmin
Figure 9.2 Diatomic model of molecular vibration. The center of gravity does not change
during the stretching vibration.
285
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9.1 Theoretical Background
9 Vibrational Spectroscopy for Molecular Analysis
(Simple
harmonic)
E
ν2
ν3 Actual diatomic
molecule
ν1
ν0
−
0
Δr
+
Figure 9.3 Potential energy (E) of diatomic molecule vibration. For a small displacement
vibration (r), the vibration motion can be treated as harmonic. Quantum theory divides
the potential energy of vibration into several levels as υ 0 , υ 1 , υ 2 , υ 3 , . . .
However, this harmonic assumption is a good approximation for molecular vibrations with small displacement. Although the potential energy is a continuous
function of the nuclear displacement, quantum mechanics tell us that the real
vibrational energy of a molecule should be quantified. For harmonic vibration, the
vibrational energy can be described
1
υ = 0, 1, 2, . . .
(9.7)
Evib = hνvib υ +
2
υ is the vibrational quantum number, which defines distinguishable vibrational
levels, as shown in Figure 9.3 and ν vib is the vibrational frequency of a molecule.
The vibrational frequency of molecules is in the range of mid-infrared (IR)
frequencies (6 × 1012 –1.2 × 1014 Hz). The ground state corresponds to υ = 0 with
corresponding vibrational energy of 12 hνvib ; the first excited level (υ = 1) should
have vibrational energy of 32 hνvib ; and so on.
Commonly, the vibrational spectroscopy covers a wave number range from
200 to 4000 cm−1 . We should know that crystalline solids also generate lattice
vibrations in addition to molecular vibrations. The lattice vibrations refer to the
vibrations of all the atoms in crystal lattice in a synchronized way. Such vibrations
exhibit lower frequencies compared with those of common molecular vibrations
and have a wave number range of about 20–300 cm−1 . Coupling between lattice
and molecular vibrations can occur if the molecular vibrations lie in such a low
wave number range. Molecular vibrations, however, can be distinguished from the
lattice vibrations because they are not as sensitive to temperature change as lattice
vibrations.
9.1.3
Principles of Vibrational Spectroscopy
9.1.3.1 Infrared Absorption
Infrared spectroscopy is based on the phenomenon of infrared absorption by
molecular vibrations. When a molecule is irradiated by electromagnetic waves
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286
within the infrared frequency range, one particular frequency may match the
vibrational frequency of the molecule (ν vib ). Consequently, the molecular vibration
will be excited by waves with the frequency ν ph = ν vib . The excitation means that
the energy of molecular vibrations will increase, normally by υ = + 1, as shown
in Eq. (9.7). In the meantime, the electromagnetic radiations with the specific
frequency ν ph will be absorbed by the molecule because the photon energy is
transferred to excite molecular vibrations. The fundamental transition from υ = 0
to υ = 1 dominates the infrared absorption, although other transitions may be
possible.
Figure 9.4 illustrates an example of the HCl diatomic molecule with
ν vib = 8.67 × 1013 Hz. When it is excited by this frequency of electromagnetic
radiation, the intensity of radiation at that frequency (8.67 × 1013 Hz) will be
reduced (absorbed) in the infrared spectrum, while the molecule itself will be
moved to a higher vibrational energy level. The absorption intensity depends on
how effectively the infrared photon energy can be transferred to the molecule. The
effectiveness of infrared absorption is discussed in detail in Section 9.3 on Raman
spectroscopy. Figure 9.5 shows an example of an infrared spectrum in which the
intensity of transmitted infrared radiation is plotted over a range of radiation wave
numbers. In the figure, an individual deep valley represents a single vibration
band that corresponds to a certain molecular vibration frequency.
9.1.3.2 Raman Scattering
Raman spectroscopy is based on the Raman scattering phenomenon of electromagnetic radiation by molecules. When irradiating materials with electromagnetic
radiation of single frequency, the light will be scattered by molecules both elastically and inelastically. Elastic scattering means that the scattered light has the same
frequency as that of the radiation. Inelastic scattering means that the scattered
light has a different frequency from that of the radiation. Elastic scattering is called
Rayleigh scattering while inelastic scattering is called Raman scattering.
Before interaction
After interaction
H
CI
Ir photons of
various frequencies
approach molecule
in ground state.
Molecule vibrationally
excited, ν = 8.67 × 1013 Hz.
One photon has been
absorbed, ν = 8.67 × 1013 Hz.
Figure 9.4 Interaction between IR radiation and a HCl molecule. HCl stretching vibration
with frequency = 8.67 × 1013 Hz absorbs the IR ray with the same frequency. (Reproduced
with permission from Ref. [2]. © 1990 Elsevier B.V.)
287
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9.1 Theoretical Background
9 Vibrational Spectroscopy for Molecular Analysis
100
% Transmittance
80
60
40
20
0
4000
3500
3000
2500
2000
1500
1000
cm–1
Figure 9.5
Typical IR absorption spectrum of hexanal. (Reproduced from Ref. [3].)
Both elastic and inelastic scattering can be understood in terms of energy
transfer between photons and molecules, as illustrated in Figure 9.6. As mentioned
before, photons of electromagnetic radiation can excite molecular vibration to a
higher level when ν ph = ν vib . If the excited vibration returns to its initial level
(Figure 9.6a), there is no net energy transfer from photons to molecular vibration.
Thus, the scattered photons from molecules will have the same frequency as the
incident radiation, similar to elastic collisions between photons and molecules. If
Virtual
Virtual
c
a
b
V=1
V=0
Anti-Stokes
Rayleigh
Stokes
Absolute frequency, ν
Figure 9.6 Elastic and inelastic scattering of incident light by molecules. Rayleigh, elastic
scattering; Stokes and anti-Stokes, and inelastic scattering. (Reproduced from Ref. [3].)
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288
the excited molecular vibration does not return to its initial level, then scattered
photons could have either lower energy or higher energy than the incident photons,
similar to inelastic collision between photons and molecules. Understandably, the
energy change corresponds to the energy difference between the initial and final
levels of molecular vibration energy. The energy changes in scattered photons
are expressed as their frequency changes. If the photon frequency decreases from
ν ph to (ν ph − ν vib ), the final energy level of molecular vibration is higher than
the initial energy (Figure 9.6b). This is called Stokes scattering. If the photon
frequency increases from ν ph to (ν ph + ν vib ), the final energy level is lower than
the initial energy (Figure 9.6c). This is called anti-Stokes scattering. The intensity of
anti-Stokes scattering is significantly lower than that of Stokes scattering. Thus, a
Raman spectrum commonly records the frequency changes caused by the Stokes
scattering by molecules. Such a frequency change (difference between radiation
and scattering frequency) is called the Raman shift in the spectrum, which should
be in the same range as the infrared absorption spectrum. Figure 9.7 shows an
example of the Raman spectrum in which the intensity of the Raman shift is plotted
over a range of wave numbers. An individual band of Raman shift corresponds to a
molecular vibration frequency. Thus, both infrared and Raman spectra are plotted
on the same scale of wave number.
9.1.4
Normal Mode of Molecular Vibrations
Understanding vibrational spectroscopy also requires basic knowledge of the
vibrational behavior of molecules. The vibrations of nuclei in a molecule can be
characterized with properties of the normal mode vibration. The normal mode
vibration of molecules has the following characteristics:
Relative scattering
intensity
• nuclei in a molecule vibrate at the same frequency and in the same phase (passing
their equilibrium positions at the same time) and
• nuclear motion does not cause rigid body movement (translation) or rotation of
molecules.
3500
2500
1500
500
Wave number (cm–1)
Figure 9.7 Typical Raman spectrum of polycrystalline graphite. (Reproduced with permission from Ref. [4]. © 1996 Elsevier B.V.)
289
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9.1 Theoretical Background
9 Vibrational Spectroscopy for Molecular Analysis
The normal mode of molecular vibrations ensures that a molecule vibrates at its
equilibrium position without shifting its center of gravity. Each type of molecule
has a defined number of vibration modes and each mode has its own frequency. We
can examine the normal modes of molecular vibration by using simple molecule
models. The simplest model of molecular vibrations is the diatomic model, which
has only one stretching mode, as shown in Figure 9.2. For polyatomic molecules,
the vibrations are more complicated. For example, a linear molecule of three atoms
connected by two bonds has a total of four vibration modes, as illustrated in
Figure 9.8. These vibration modes include two stretching modes and two bending
modes. One stretching mode is symmetric (v1 in Figure 9.8) because the two bonds
are stretched simultaneously. Another stretching mode is asymmetric (v3 in Figure
9.8) because one bond is stretched while the other is compressed. A bending mode
changes the angle between two bonds, but not the bond lengths. The two bending
modes are notated as ν 2 and ν 4 in Figure 9.8. One is bending in the plane of the
figure and the other is in the horizontal plane.
Two features of bending modes can be revealed from the molecule model
in Figure 9.8. First, the bending vibration can occur in an infinite number of
planes that are in neither the figure plane nor the horizontal plane. However,
we can ‘‘decompose’’ any bending mode and express it in terms of v2 and v4 ,
as for decomposing a vector. Secondly, the two bending modes in Figure 9.8 are
indistinguishable in terms of frequency, because the relative movements of nuclei
in the two bending modes are physically identical. These two bending vibrations
with the same physical identity are the degenerate vibrations.
Normal vibration modes of a triatomic molecule with a bending angle are
illustrated in Figure 9.9. There are three normal modes in this molecule: symmetric
stretching, asymmetric stretching, and bending in the plane of the figure. Bending
in the horizontal plane, similar to Figure 9.8, will generate rotation of the molecule,
which is not considered as a vibration.
O
C
ν1
O
O
C
O
Asymmetric
stretch
Symmetric
stretch
O
C
ν3
−
O
O
+
C
−
O
ν2, 4
Bend
degenerate pair
Figure 9.8
Normal modes of vibrations in a CO2 molecule. (Reproduced from Ref. [3].)
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290
Symmetric
stretch
3652 cm–1
Asymmetric
stretch
3756 cm–1
Bend
1595 cm–1
Figure 9.9 Normal modes of vibrations in a H2 O molecule. (Reproduced from Ref. [3].)
9.1.4.1 Number of Normal Vibration Modes
It is necessary for us to know how to count the number of normal vibration
modes in a molecule. The total number of vibration modes relates to the degrees
of freedom in molecular motion. For N atomic nuclei in a molecule, there are 3N
degrees of freedom because each nucleus can move in x, y, or z directions in a
three-dimensional space. Among the 3N degrees of freedom, however, there are
three related to translation of a molecule along x, y, or z direction as a rigid body
without stretching any bond connecting nuclei or changing any bond angle. Also,
there are 3 degrees of freedom related to rotate a molecule around the x, y, or z
axes as a rigid body. The molecular vibrations are related only to internal degrees
of freedom in a molecule without translation and rotation of the rigid body. Thus,
the total vibration modes of an N-atomic molecule should be 3N − 6. For a linear
molecule, the rotation around the bond axis is meaningless, considering the nuclei
as points in space. Thus, there are only two rotational degrees of freedom for the
molecule, and the total vibration modes should be 3N − 5 for a linear molecule.
For example, the linear molecule of CO2 should have 9 − 5 = 4 vibration modes, as
shown in Figure 9.8.
9.1.4.2 Classification of Normal Vibration Modes
It is possible to categorize the various modes of molecular vibration modes into
four types:
1) stretching vibration (ν);
2) inplane bending vibration (δ);
3) out-of-plane bending vibration (γ ); and
4) torsion vibration (τ ).
Table 9.1 summarizes the features of the four vibration types. The last three types
only change the bond angles, but do not stretch bonds. The torsion vibration can be
considered as a special type of bending vibration, as illustrated in Table 9.1. Thus,
we can simply say that a vibration is either the stretching or the bending type. γ and
τ only occur in molecules that have at least three bonds. Generally, the vibration
frequency varies with vibration type. The frequency decreases with increasing
291
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9.1 Theoretical Background
Table 9.1
9 Vibrational Spectroscopy for Molecular Analysis
Basic types of molecular vibrations.
Type
Stretching vibrations
Bending vibrations
Inplane
Torsion vibrations
Out-of-plane
−
+
a
Schematic
Symbol
Minimum number of bonds
ν
1
−
δ
2
γ
3
+
−
τ
3
Data reproduced from Ref. [1].
number of bonds involved. Special types of vibrations may occur in a larger
molecule like in a polymer; however, they all can be derived from these four basic
types.
9.1.5
Infrared and Raman Activity
Among the total number of normal vibration modes in a molecule, only some
can be detected by infrared spectroscopy. Such vibration modes are referred to
as infrared active. Similarly, the vibration modes that can be detected by Raman
spectroscopy are referred to as Raman active. Consequently, only active modes
can be seen as vibration bands in their respective infrared or Raman spectra.
For example, Figure 9.10 shows the infrared and Raman spectra of chloroform
molecules. The infrared and Raman spectra complement each other, as shown
in Figure 9.10. The principles of infrared and Raman activity are complicated;
thorough understanding requires group theory of mathematics. Nevertheless, it is
Transmittance
4000 cm–1 3000
2000
1500
1000
500
1500
1000
500
200
CHCI3
Infrared
Intensity
Raman
4000 cm–1 3000
CHCI3
2000
0
Figure 9.10 Comparison of IR and Raman spectrum with the example of CHCl3 molecules
(Reproduced with permission from Ref. [2]. © 1990 Elsevier B.V.)
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292
possible to understand the basic ideas without the group theory, as presented in
the following sections.
9.1.5.1 Infrared Activity
To be infrared active, a vibration mode must cause alternation of dipole moment
in a molecule. A molecule has a center of positive charge and a center of negative
charge. If these two centers are separated by a distance (l), the dipole moment (μ)
is defined
μ = el
(9.8)
e represents the amount of electrical charge at the charge center of the molecule.
A molecule may exhibit a permanent dipole moment with separated positive and
negative centers, or zero dipole moment with superimposed centers. The infrared
activity requires changes in the magnitude of normal vibration during the vibration.
The magnitude is commonly represented with a parameter q (which is equivalent
to |r| in Eq. (9.5)).
Mathematically, the requirement of infrared activity is expressed as the derivative
of dipole moment with respective to the vibration at the equilibrium position is not
zero.
∂μ
= 0
(9.9)
∂q q=0
It does not matter whether the molecule has a permanent dipole moment, because
the dipole moment can be induced by the electric field of an electromagnetic wave.
For example, if plotting the changes in dipole moment versus vibration modes of
CO2 , as in Figure 9.11a, we find that vibration modes ν 2 , ν 3 , and ν 4 are infrared
active, but not ν 1 (see Figure 9.8 for the CO2 vibration modes).
(a)
μ
ν2, 4
(b)
α
ν1
ν2, 4
q
q
ν1
ν3
ν3
Figure 9.11 CO2 molecule vibrations: (a) dipole moment (μ) as a function of vibration
displacement (q); and (b) polarizability (α) as a function of vibration displacement (q).
(Reproduced from Ref. [3].)
293
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9.1 Theoretical Background
We can understand more about the infrared activity from Figure 9.12. The HCl
molecule (Figure 9.12a) has a permanent dipole. Its stretching vibration is infrared
active because the dipole distance changes during stretching vibration. The H2
molecule (Figure 9.12b) has a center of symmetry and a zero dipole moment. It is
infrared inactive, because the centers of positive and negative charge always remain
as the center of symmetry and the dipole moment is always equal to zero during
vibration. The CO2 molecule also has a center of symmetry and zero dipole moment
at equilibrium (Figure 9.12g). Its symmetric stretching is infrared inactive, similar
to the case of H2 (Figure 9.12c). However, its asymmetric stretching (Figure 9.12d)
cannot retain the center of symmetry and change of dipole moment from 0 to a
certain value. Similarly, the bending vibration (Figure 9.12e) also induces a nonzero
dipole moment during vibration. Thus, these two vibration modes are infrared
active. The principle of vibration activity also applies to ion groups. For example,
symmetric stretching of (CO3 )2− (Figure 9.12i) is infrared inactive because the
centers of negative charge from three negatively charged oxygen ions always
coincide with the center of positive charge from carbon. However, asymmetric
(a)
+
−
(b)
H
CI
H
+
CI
−
(c)
H
+
+
+
+
H
H
(d)
(e)
O
O
+
−
−
+
C
O
C
O
O
Center of
symmetry
(f)
O
C
H
H
O
− +
(g)
O
O
O
+
+
C
H
C
C
+
+
C
O
O
O
+ −
+
+
(h)
O
+
+
(i)
+
−
O
O
O
O
C
O
O
O
C
O
Figure 9.12 Dipole moment changes during vibration of several molecules: (a) HCl
stretching; (b) H2 stretching; (c) H2 center
of symmetry; (d) CO2 asymmetric stretching; (e) CO2 bending; (f) CO2 symmetric
−
+
+
+
O
+
+
+
+
C
C
O
+
+
O
stretching; (g) CO2 center of symmetry; (h)
CO3 asymmetric stretching; and (i) CO3
symmetric stretching. (Reproduced with permission from Ref. [2]. © 1990 Elsevier B.V.)
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9 Vibrational Spectroscopy for Molecular Analysis
294
stretching of (CO3 )2− (Figure 9.12h) is infrared active. The bending vibrations of
(CO3 )2− , which are not shown in Figure 9.12, should also be infrared active.
9.1.5.2 Raman Activity
To be Raman active, a vibration mode must cause polarizability changes in a
molecule. When a molecule is placed in an electric field, it generates an induced
dipole because its positively charged nuclei are attracted toward the negative pole
of the field and its electrons are attracted toward the positive pole of the field.
Polarizability (α) is a measure of the capability of inducing a dipole moment (μ) by
an electric field. It is defined in the following equation
μ = αE
(9.10)
E is the strength of electric field. Polarizability determines the deformability of the
electron cloud of a molecule by an external electric field, similar to the compliance of
elastic deformation. Mathematically, Raman activity requires that the first derivative
of polarizability with respect to vibration at the equilibrium position is not zero.
∂α
= 0
(9.11)
∂q q=0
Again, using CO2 as the example, Figure 9.11b shows the change of α with respect
at q = 0 is not zero.
to q and shows us that only v1 is Raman active because ∂α
∂q
Polarization of molecules varies with directions in a three-dimensional space. For
example, in a linear molecule such as CO2 , the electron cloud has the shape of an
elongated watermelon. Such an electron cloud is more deformable along its long
axis than the directions perpendicular to the long axis. The Raman activity can
be illustrated using the changes of the polarizability ellipsoid that represents the
polarizability variation in three-dimensional space. The ellipsoid has the dimension
of α i − 1/2 (the distance between the ellipsoid origin to ellipsoid surface in direction
i), as shown in Figures 9.13 and 9.14.
Generally, if the ellipsoid changes its size, shape, and orientation with vibration,
that vibration is Raman active.
Figure 9.13 illustrates the change of the polarizability ellipsoid in normal mode
vibrations of the H2 O molecule. Its ν 1 , ν 2, and ν 3 modes are all Raman active
because the ellipsoid changes size, shape, or orientation, as shown in Figure 9.13.
We should interpret the ellipsoid change with caution. Some modes with apparent
ellipsoid change with vibrations are not Raman active. For example, the change of
the polarizability ellipsoid in CO2 vibrations (Figure 9.14) does not mean Raman
activity in all modes. The symmetric stretching model, ν 1 , of CO2 is Raman active
because the ellipsoid size changes during vibration. However, ν 2 and ν 3 of CO2
are not Raman active, even though the ellipsoid changes during vibrations. The
problem is that ellipsoid change is symmetric in + q and − q. Such displacement
symmetry with respect to the equilibrium position makes the following expression
zero.
∂α
=0
(9.12)
∂q q=0
295
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9.1 Theoretical Background
9 Vibrational Spectroscopy for Molecular Analysis
+q
−q
q=0
O
O
H
H
H
H
O
H
H
ν1
O
H
O
O
H
H
H
H
H
ν2
O
H
O
H
H
O
H
H
H
ν3
Figure 9.13 Normal modes of H2 O vibrations and changes in polarizability ellipsoids.
ν 1 , ν 2 , and ν 3 are all Raman active. (Reproduced with permission from Ref. [5]. © 2003
Elsevier B.V.)
+q
O
−q
q=0
C
O
O
C
O
O
C
O
O
C
O
O C O
ν1
O
C
O
O
C
O
ν3
C
O
O
O
C
O
ν2
Figure 9.14 Normal modes of CO2 vibrations and changes in polarizability ellipsoids. ν 1
is Raman-active but ν 3 , ν 2 , and ν 4 are not. (Reproduced with permission from Ref. [5]. ©
2003 Elsevier B.V.)
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296
1.
4.
2.
5.
3.
Figure 9.15 Five normal modes of vibrations in acetylene H–C≡C–H. (Reproduced with
permission from Ref. [2]. © 1990 Elsevier B.V.)
Figure 9.11b clearly illustrates such a situation of ν 2 , ν 3, and ν 4 . The example of
acetylene may further help our understanding. Figure 9.15 shows the two extreme
positions of each vibration: 1, 2, 3, 4, and 5 in the linear acetylene molecule
(H–C≡C–H). The vibrations 1, 2, and 3 are Raman active, but not 4 and 5. In
vibrations 1 and 2, the molecular shape is different in the two extreme positions of
vibrations. Thus, the polarizability ellipsoid will change its size or shape, similar to
the ν 1 mode of CO2 . In vibration 3, the shape is identical at its two extreme positions,
but there is an orientation change in its ellipsoid. The ellipsoid orientation change
results from the clockwise and counterclockwise rotation of C≡C and C–H bonds.
In vibrations 4 and 5, the polarizability ellipsoid does not change its size and shape
because their two extreme positions are identical. Vibration 5 does not cause the
ellipsoid orientation to change either, because the clockwise rotation of one C–H
bond is compensated for by the counterclockwise rotation of another C–H bond.
In summary, we can highlight the features of infrared- and Raman-active
vibrations:
• a vibration can be one of three cases: infrared-active, Raman-active, or both
infrared- and Raman-active and
• in molecules that have a center of symmetry, infrared-, and Raman-active
vibrations are mutually exclusive.
Further, it is helpful for us to know that vibrations of ionic bonds are strong in
infrared spectroscopy (for example, O–H), and vibrations of covalent bonds are
strong in Raman spectroscopy (for example, C=C).
9.2
Fourier Transform Infrared Spectroscopy
FTIR is the most widely used vibrational spectroscopic technique. FTIR is an
infrared spectroscopy in which the Fourier transform method is used to obtain an
infrared spectrum in a whole range of wave numbers simultaneously. It differs
from the dispersive method that entails creating a spectrum by collecting signals
297
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
at each wave number separately. Currently, FTIR has almost totally replaced the
dispersive method because FTIR has a much higher signal-to-noise ratio than that
of the dispersive method.
9.2.1
Working Principles
The key component in the FTIR system is the Michelson interferometer, as schematically illustrated in Figure 9.16. The infrared radiation from a source enters the
Michelson interferometer. The interferometer is composed of one beamsplitter
and two mirrors. The beamsplitter transmits half of the infrared (IR) beam from
the source and reflects the other half. The two split beams strike a fixed mirror
and a moving mirror, respectively. After reflecting from the mirrors, the two split
beams combine at the beamsplitter again in order to irradiate the sample before
the beams are received by a detector.
The function of the moving mirror is to change the optical path lengths in order
to generate light interference between the two split beams. If the moving mirror is
located at the same distance from the beamsplitter as the fixed mirror, the optical
paths of the two split beams are the same; thus, there is zero path difference. An
optical path difference (δ) will be introduced by translating the moving mirror
away from the beamsplitter. Changing the optical-path difference is similar to what
happens in diffraction of crystallographic planes (Figure 2.6). The two split beams
will show constructive and destructive interference periodically, with continuous
change of δ value. There will be completely constructive interference
when δ = nλ,
but completely destructive interference when δ = 12 + n λ. A change of δ value
is realized by a change in the position of the moving mirror, as illustrated in
Figure 9.16.
A plot of light interference intensity as a function of optical path difference is
called an interferogram. Figure 9.17 illustrates interferograms of a radiation with two
wavelengths λ and 3λ. The interferogram at the top is the sum of interferograms of
Source
Beamsplitter
Infrared
radiation
Detector
Moving mirror
Sample
Fixed mirror
Figure 9.16
Optical diagram of a Michelson interferometer in FTIR.
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298
Intensity
λ + 3λ
3λ
λ
Optical path difference
Figure 9.17 Interferograms: the bottom curve is the interferogram of light with wavelength
λ and the middle curve is the interferogram of light with wavelength 3λ; and the top one is
the sum of two beneath it. (Reproduced with permission from Ref. [6]. © 1996 CRC Press
LLC.)
Arbitray Y
Voltage
Fourier Transform
Optical path difference (cm)
4000
3000
2000
1000
Wave number (cm–1)
Figure 9.18 Plots of an interferogram (left one) and its Fourier transform from an interferogram to an IR spectrum (right one). (Reproduced with permission from Ref. [6]. © 1996
CRC Press LLC.)
two light waves with wavelength λ and 3λ. The IR radiation from the FTIR source
is composed of numerous wavelengths. An interferogram of an FTIR looks like
that in Figure 9.18a. It has a sharp center burst that dies off quickly into two wings.
The center burst corresponds to the position of the moving mirror generating zero
path difference at which the interferogram has the maximum intensity because all
the waves have completely constructive interference (in phase). An interferogram
299
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
irradiating the sample is the sum of sinusoidal waves with a range of wavelengths.
The FTIR detector receives interferogram signals that are transmitted through a
sample (or reflected from a sample). The interferogram received by the detector is
not an infrared spectrum.
Fourier transformation is necessary to convert an interferogram into an infrared
spectrum, which is a plot of the light intensity versus wave number, as shown
in Figure 9.18b. The Fourier transform is based on a fact that any mathematical
function can be expressed as a sum of sinusoidal waves. All the information of wave
intensity as a function of wavelength is included in the sum of sinusoidal waves. A
computer equipped with a FTIR instrument constructs the infrared spectrum using
a fast Fourier transform (FFT) algorithm that substantially reduces the computation
time.
The Fourier transform as a mathematical tool has been mentioned in Chapter 3
when discussing the relationship between real space and reciprocal space. Here, it
is emphasized as a tool that transfers information between a function in the time
(t) domain and its corresponding one in the frequency (ω) domain.
∞
1
f (t)e−iωt dt
(9.13)
F(ω) = √
2π −∞
In an FTIR instrument, the Fourier transform converts the intensity versus optical
path difference to the intensity versus wave number. The optical path difference
can be considered as in the time domain because it is obtained by multiplying time
with the speed of a moving mirror. The wave number can be considered as in the
frequency domain because it is equal to frequency divided by the light speed.
9.2.2
Instrumentation
9.2.2.1 Infrared Light Source
The infrared light source generates wideband radiation by heating solid materials
to incandescence using electric power. There are two commonly used IR sources:
the Nernst glower, which is composed of mainly oxides of rare-earth elements; and
the Globar, which is composed of silicon carbide. The range of IR wavelength and
energy distribution is highly temperature sensitive as shown in Figure 9.19. Most
IR sources are operated at the temperature where the maximum energy of radiation
is near the short-wavelength limit of the IR spectrum.
9.2.2.2 Beamsplitter
Beamsplitters should be made of material semitransparent to infrared light.
Beamsplitters should reflect a one-half portion of infrared light to the moving
mirror while transmitting the rest to a fixed mirror. The most common beamsplitter
has a sandwich structure, with a thin layer of germanium (Ge) between two pieces
of potassium bromide (KBr); it works well in the wave number range 4000 to
400 cm−1 . Ge is able to split infrared light. KBr is a good substrate material because
it is transparent to infrared light, yet has good mechanical strength. It functions
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300
Eλ, watts/cm2/micrometer
4
1000 °C
3
800 °C
2
Area - Eλdλ
1
600 °C
Eλ
λm = 2.276
0.5 1
2
3
4
dλ
5
6
7
8
Wavelength, micrometers
Figure 9.19 Energy distributions of IR source with continuous wavelength radiation. Most
IR sources are operated at a temperature where the energy maximum is near the shortwavelength limit of the IR spectrum. (Reproduced with permission from Ref. [2]. © 1990
Elsevier B.V.)
as a protective coating for the Ge. The drawback of using KBr as a substrate is its
hygroscopic nature. KBr tends to absorb water vapor from the atmosphere and fog
readily forms on it. Thus, all FTIR instruments require low humidity or are sealed
from atmosphere. The low humidity environment around the beamsplitter can be
obtained by purging with dry air or nitrogen. More conveniently, the instrument is
sealed such that the infrared beam passes through a window to reach the sample.
9.2.2.3 Infrared Detector
The infrared detector is a device to measure the energy of infrared light from
the sample being examined. It functions as a transducer to convert infrared light
signals to electric signals. There are two main types: the thermal detector and the
semiconductor detector. The key component in a thermal detector is a pyroelectric
crystal, of which the most commonly used type is deuterated triglycine sulfate (DTGS).
Infrared radiation causes a temperature change in DTGS that, in turn, changes
its dielectric constant. This dielectric constant affects its capacitance and results
in a voltage change across the DTGS. The DTGS detector operates in the wave
number range 4000 to 400 cm−1 . It is simple and inexpensive but less sensitive than
the semiconductor detector. The most commonly used semiconductor detector is
made of mercury cadmium telluride (MCT). An MCT detector absorbs infrared
photons which in turn causes the electrons to migrate from the valence band
to the conduction band of the semiconductor. The electrons in the conduction
band generate electric current signals. The MCT detector is up to 10 times more
sensitive than the DTGS type; however, it detects a narrower band of radiation
(4000 to 700 cm−1 ). The MCT detector needs to be cooled, commonly to liquid
nitrogen temperature (−196 ◦ C), before operation. Another disadvantage of MCT
is that it saturates easily with high intensity radiation. This can be a problem for
quantitative analysis.
301
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
9.2.2.4 Fourier Transform Infrared Spectra
An infrared spectrum converted from an interferogram by Fourier transform
is called a single-beam spectrum. A single-beam spectrum includes both spectra
from the sample and background. The background spectrum contains only the
information from the instrument and atmosphere, not from the sample being
examined. The instrument contributions to background spectrum are from the
detector, beamsplitter, mirror, and the IR source. The atmospheric contributions
are mainly from water vapor and carbon dioxide. Figure 9.20 demonstrates how significant background can be to the IR spectrum. Figure 9.20a shows a simple-beam
(a)
(b)
2.5
40
30
Arbitrary Y
1.5
1.0
20
0.5
10
0.0
0
4000 3500 3000 2500 2000 1500 1000 500
4000
(c)
3000
2000
1000
Wave number (cm–1)
Wave numbers
Transmittance
Response
2.0
90
80
70
60
50
4000 3500 3000 2500 2000 1500 1000 500
Wave number
Figure 9.20 (a) Single-beam FTIR spectrum of background: a plot of raw detector response versus wave number without
a sample; (b) a sample single-beam FTIR
spectrum of polystyrene (vibrational bands of
polystyrene are superimposed on background
spectrum); and (c) final FTIR spectrum of
polystyrene that only contains the vibration
bands from the polystyrene sample (absorption intensity is expressed as the transmittance). (Reproduced with permission from
Ref. [6]. © 1996 CRC Press LLC.)
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302
spectrum of a polystyrene sample. Figure 9.20b shows a single beam spectrum of
the chamber without the polystyrene sample, which is a background spectrum. In
the background spectrum, typical water vapor bands at around 3500 and 1630 cm−1
and CO2 gas bands at 2350 and 667 cm−1 are visible. To eliminate the background
influence, the ratio of the single-beam spectrum of a sample to the background
spectrum should be made. This process results in a transmittance spectrum as
shown in Figure 9.20c. Transmittance (T) is defined as the ratio of intensities
T = I/Io
(9.14)
I is the intensity measured in a single-beam spectrum of sample and Io is the
intensity measured in the background spectrum. Transmittance is often expressed
as %T, which forms the scale of the vertical axis in Figure 9.20c. The spectrum can
also be presented as absorbance (A) versus wave number as shown in Figure 9.21.
The absorbance is calculated from the transmittance.
A = − logT
(9.15)
An FTIR spectrum is commonly expressed as a transmittance spectrum,
in which vibration band peaks point downward. It can also be expressed
as an absorbance spectrum, in which vibration band peaks point upward
(Figure 9.21). For quantitative analysis, an absorbance spectrum should be used
Absorbance
1
.5
0
4000
3000
2000
1000
Wave number (cm–1)
Figure 9.21 FTIR spectrum where the absorption intensity is expressed as absorbance.
In this spectrum the absorbance scale is normalized to a range 0–1. (Reproduced with
permission from Ref. [6]. © 1996 CRC Press LLC.)
303
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
because the peaks of a transmittance spectrum are not linearly proportional to
concentration.
9.2.3
Examination Techniques
9.2.3.1 Transmittance
The transmittance examination technique refers to the method of obtaining an
infrared spectrum by passing an IR beam through a sample, as illustrated in
Figure 9.16. It is the most commonly used examination method in FTIR for two
reasons. First, the transmittance technique generates high signal-to-noise ratios,
and secondly, it is suitable for samples in any of solid, liquid, or gas phases. Its main
disadvantage is the thickness limitation of samples. A thick sample will absorb
so much of the infrared radiation that detecting infrared transmission becomes
impossible. Generally, for transmission examination, the sample thickness should
not be more than 20 μm. On the other hand, a sample that is too thin (< 1 μm)
yields absorption bands too weak to be detected.
9.2.3.2 Solid Sample Preparation
Solid samples for transmittance examination can be in one of two forms: thin film
or powder. Thin-film samples are mainly polymeric materials. Casting films with
polymer solutions is a commonly used method. Polymer films can also be made by
mechanical pressing under elevated temperatures. Powder samples are made by
grinding solid to powder and then diluting the powder with infrared-inert matrix
materials. There are two typical methods for preparing powder samples: making
KBr pellets and making mulls. As mentioned in the instrumentation section, KBr
is transparent to infrared light. To make pellets, we grind a solid sample with KBr
together to obtain powder particles with size less than 2 μm diameter. Then, the
powder mixture is die-pressed to form a pellet. For the mull method, a solid sample
is ground to a powder and then diluted with a mulling agent (usually mineral oil).
The slurry of powder–oil is smeared on a KBr plate and sandwiched with another
KBr plate. The mull method is simple and inexpensive; however, the mulling agent
contains long and straight chains of hydrocarbons, which absorb strongly around
3000 and 1400 cm−1 , and hence it may complicate the sample spectrum.
9.2.3.3 Liquid and Gas Sample Preparation
Liquid and gas samples do not need much preparation, but special cells to contain
the samples are often necessary. The simplest method to prepare a liquid sample
is to make a capillary thin film of the liquid. The capillary thin film is made by
placing a drop of liquid on a KBr plate and sandwiching it with another KBr plate.
This method, however, is not suitable for volatile liquids. Liquid cells can be used
for volatile liquid and toxic liquid samples, particularly for quantitative analysis.
The spacing between the bottom and the top of a liquid cell is typically from 1
to 100 μm. The cell is made of an infrared-transparent material. Typically, KBr is
used; however, KBr should not be selected as the material for holding samples
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304
containing water because water dissolves KBr. Instead, ZeSe or AgCl should be
used because they are infrared-transparent but not water soluble. Cells for gas
samples are structurally similar to cells for liquid but the dimension is much
larger.
9.2.3.4 Reflectance
Reflectance examination techniques refer to methods for obtaining an infrared
spectrum by reflecting IR radiation from a solid or liquid sample. The main
advantage is that bulk and coating samples can be examined without destructive
preparation. These techniques are especially attractive for solid samples that
are difficult to grind into powder and for fast sample examination. However,
reflectance techniques are less popular than transmission because of their following
disadvantages. First, infrared radiation has limited penetration into the sample.
A reflectance spectrum can only contain the infrared signals from the top 1 to
10 μm of a solid sample surface. This is a serious deficiency for a sample with
possible chemical composition change near its surface, and for quantitative analysis
for which the exact pass-length of infrared light in the sample must be known.
Secondly, it is more difficult to capture reflected infrared light than transmitted
light. A reflectance spectrum will show much more noise than the transmission
spectrum for the same duration of examination. Thirdly, reflectance techniques
require special accessories, making the instrumentation more complicated and
expensive.
There are three types of reflectance techniques: specular, diffuse, and
reflection–absorption, as illustrated in Figure 9.22. Specular reflectance is
applied to samples with smooth and polished surfaces, diffuse reflectance is
applied to samples with rough surfaces, and reflection–absorption is applied
to IR-transparent thin films on IR opaque substrates. The specular and diffuse
techniques are more widely used and are introduced in more detail in the following
text.
Specular reflectance occurs when an incident infrared beam strikes a smooth
surface of a solid sample. The reflectance angle is the same as the incidence angle
during specular reflectance. The optical arrangement of the specular reflectance
accessory is schematically shown in Figure 9.23. It consists of two flat mirrors and
a platform with a hole. The sample is placed over the hole in the platform. The
background spectrum is obtained by placing an ‘‘ideal reflector’’ of infrared light,
such as a gold or aluminum mirror, over the hole. The optical arrangement is
Specular
Reflection
absorption
Figure 9.22 Reflectance types in FTIR spectroscopy.
Diffuse
305
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
Sample
To detector
IR beam
Flat mirrors
Figure 9.23 Optical diagram of a simple specular reflectance accessory for FTIR
instrument.
also applied to a reflection–absorption case where there is reflectance on a smooth
substrate coated with a thin film. In such case, the infrared beam goes through a
double transmission through the coating film. To obtain a background spectrum for
examining the coating film, the smooth surface of substrate material is placed over
the platform hole.
Diffuse reflectance occurs when an incident infrared beam strikes a rough
surface; the surface could be solid, powder, or even liquid. The reflectance angle
spreads over a wide range during diffuse reflectance. The optical arrangement of
accessories for measuring diffuse reflectance consists of a focusing mirror, two flat
mirrors and a sample cup, as shown in Figure 9.24. The focusing mirror collects
infrared light reflected off the sample. The sample cup can hold either powder or
liquid samples. Diffuse reflectance can be used to examine a sample of microgram
mass. It can also be used to examine intractable objects such as a large piece of
plastic. Another method for preparing samples for diffuse reflectance examination
is to take a piece of abrasive paper with silicon carbide particles and rub the surface
of the object to be examined. The abrasive paper will be covered with a certain
amount of sample material. Then, we can place the abrasive paper in the sample
cup for FTIR examination.
To detector
Mirror
Figure 9.24
IR beam
Sample/KBr
mixture
Mirror
Optical diagram of a diffuse reflectance accessory for an FTIR instrument.
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306
9.2.4
Fourier Transform Infrared Microspectroscopy
FTIR spectroscopy can combine with microscopy for generating FTIR spectra from
microscopic volumes in materials. The instrument for FTIR microspectroscopy is
simply called the FTIR microscope, which is often attached to the conventional FTIR
instrument. The FTIR microscope is increasingly used for materials characterization because of its simple operation and FTIR spectra can be collected rapidly from
microscopic volumes selected with the microscope.
9.2.4.1 Instrumentation
The FTIR microscope has an optical system that can easily switch between visible
light observation and infrared light spectroscopy. Also, the microscope can be
operated in either transmittance or reflectance modes in order to meet the sample
conditions, either transparent or opaque to light. The microscope has two light
sources: a visible light source and an infrared light source. It also has an infrared
detector and video camera or eyepieces, like a regular light microscope. However,
there is only one system of condenser and objective lens.
Figure 9.25 illustrates the optical paths of the microscope in the modes for FTIR
spectroscopy. Figure 9.25a shows the optical path of the infrared beam when the
microscope operates in the transmittance mode, while Figure 9.25b shows the
optical path in the reflectance mode. We should note that lenses used in FTIR
differ from those used in conventional light microscopes. The lenses used in FTIR
microscopy are the Cassegrain type. The Cassegrain lens is composed of curved
mirrors, not transparent glass pieces. Light passing the Cassegrain lens is reflected
by a larger mirror with a parabolic shape and a smaller mirror with a hyperbolic
shape for collection and focus of the beam, respectively. The Cassegrain lens is
preferred for the reflecting lens in the FTIR microscope because it does not absorb
the energy of infrared light as a conventional optical lens does. The lens does not
possess chromatic aberration either. The power of the Cassegrain objective used in
a FTIR microscope is relative low, usually less than 10×.
The selection of the microscopic area for FTIR microspectroscopy is achieved by
a remote aperture located between the objective and detector. The remote aperture
commonly has a rectangular opening with two pairs of knife-edged blades. The
blades are often made from a material that is transparent to visible light but opaque
to infrared light.
The infrared detector in the FTIR microscope must be highly efficient, such as the
MCT detector. The IR radiation intensity from a microscopic area is significantly
lower than from the sample in a conventional FTIR instrument. The MCT detector
can ensure a sufficiently high signal-to-noise ratio for meaningful IR spectroscopy.
The drawback of using the MCT detector is the requirement of low temperature
operation at −196 ◦ C. It usually takes more than 8 h to cool the MCT detector to
the operating temperature using liquid nitrogen.
307
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
Optical
microscope
(a)
MCT detector
MCT cassegrain
Detector mirror
Remote
aperture
M2
M4
C2
Sample
position
C1
M3
Base of microscope
(b)
MCT detector
MCT cassegrain
Optical
microscope
Detector mirror
Remote
aperture
M4
C2
M2
Sample
position
C1
M3
Base of microscope
Figure 9.25 Optical paths of FTIR microscope with IR radiation: (a) transmittance and (b)
reflectance. M, mirror; C, Cassegrain lens. (Reproduced by permission of PerkinElmer Inc.)
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308
9.2.4.2 Applications
In principle, operation of the FTIR microspectroscopy is the same as for a
conventional FTIR instrument except the spectrum is obtained from a microscopic
area or intensity distribution is mapped in the sample plane. A spectrum from
an area in the order of 10 × 10 μm can be obtained. Mapping or FTIR imaging
at microlevel resolution can be achieved by scanning a sample using a motorized
sample stage. The resolution is primarily determined by the size of the focused
IR beam and the precision of the motorized stage. Reflectance microspectroscopy
is more widely used than the transmittance mode in FTIR microscopy because
minimal sample preparation is required.
Figures 9.26 and 9.27 illustrate an example of using the FTIR microscope to
identify a microsized particle. A contaminant particle is isolated, as shown in the
AM
C
100 μ m
Figure 9.26 Micrograph of isolated particulate contamination (AM) and cotton fiber (C).
(Reproduced with permission from Ref. [7]. © 1995 Taylor & Francis Group Ltd.)
1.0
0.8
0.6
Absorbance
0.4
0.2
−0.0
−0.2
−0.4
−0.6
−0.8
4000 3500 3000 2500 2000
1800
1600
1400
Wave numbers
1200
1000
800
Figure 9.27 IR spectrum of the isolated particle (lower) and IR spectrum of polystyrene
(upper). (Reproduced with permission from Ref. [7]. © 1995 Taylor & Francis Group Ltd.)
309
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9.2 Fourier Transform Infrared Spectroscopy
9 Vibrational Spectroscopy for Molecular Analysis
micrograph (Figure 9.26). The twisted fiber is cotton. The particle attached to the
fiber was examined with reflectance FTIR microspectroscopy. Figure 9.27 shows
the IR spectrum of the particle and its identification as polystyrene by comparing
the experimental spectrum with the standard polystyrene spectrum.
9.3
Raman Microscopy
Raman microscopes are more commonly used for materials characterization than
other Raman instruments. Raman microscopes are able to examine microscopic
areas of materials by focusing the laser beam down to the micrometer level
without much sample preparation, as long as a surface of the sample is free from
contamination. This technique should be referred to as Raman microspectroscopy
because Raman microscopy is not mainly used for imaging purposes, similar
to FTIR microspectroscopy. An important difference between Raman and FTIR
microspectroscopies is their spatial resolution. The spatial resolution of the Raman
microscope is at least 1 order of magnitude higher than the FTIR microscope.
Raman microspectroscopy (often called micro-Raman), like most Raman spectrometry, is of the dispersive type. It requires collecting a spectrum at each wave
number separately, not like the FTIR type that collects a spectrum in a range of wave
numbers simultaneously. Although this chapter only describes the instrumentation for Raman microscopy, its working principles are basically the same as those
of conventional dispersive Raman instruments, which consist of the following
elements:
•
•
•
•
laser source;
sample illumination and collection system;
spectral analyzer; and
detection and computer control and processing system.
Raman spectroscopy requires highly monochromatic light, which can be provided
only by a laser source. The laser source is commonly a continuous-wave laser, not
a pulsed laser. The laser source generates laser beams with the wavelengths in the
visible light range or close to the range. In a micro-Raman, sample illumination and
collection are accomplished in the microscope. The microscope’s optical system
enables us to obtain a Raman spectrum from a microscopic area: this is the main
difference between the micro-Raman and conventional Raman spectrometers.
9.3.1
Instrumentation
The optical arrangement of a Raman microscopic system is schematically illustrated
in Figure 9.28. A laser beam passes through a filter to become a single-wavelength
beam, which is then focused on a sample surface by the microscope. The Raman
scattered light reflected from a microscopic area of sample is collected by the
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310
Microscope
Sample
Holographic
filters
Diffraction
grating
Slit
CCD camera
B
A
Beam expander
Source
Figure 9.28 Optical diagram of a Raman microscope.
microscope and sent to the detector. The Raman scattered light, which results
from inelastic scattering, is weak compared with the incident laser light. Thus, a
holographic filter has to be used in order to block the laser light entering the detector
system. The wavelength of Raman scattering light is selected by a diffraction grating
system before being recorded by a detector. More details of the optical components
in a Raman microscopic system are presented below.
9.3.1.1 Laser Source
Commonly used laser sources are gas continuous-wave lasers such as Ar+ , Kr+ ,
and He–Ne. Such laser sources are often capable of generating beams of multiple
wavelengths. For example, Ar+ generates a range of wavelengths with different
intensities. The highest intensity wavelengths include 515.4, 488.0, and 350.7 nm.
Thus, it is necessary to filter out wavelengths other than 515.4 nm when an Ar+
laser is used. The He Ne laser, however, generates beams of only one wavelength at
632.8 nm. Gas laser sources generate several tens of milliwatts of laser power, but
the laser power reaching the microscopic area of the sample is only about 5 mW.
9.3.1.2 Microscope System
The microscope in the Raman system is different from conventional microscopes
used for observation of microstructure in two aspects: the microscope only needs
to illuminate a microscopic area, not the entire field, and the microscope must
have a high numerical aperture (NA) in order to collect the Raman-scattered light
over a large solid angle effectively. The schematic layout in Figure 9.29 illustrates
the optical features of the Raman microscope. The beam from the laser source is
first filtered to obtain a monochromatic wavelength. Then, a pinhole spatial filter
removes the appearance of the diffraction rings and speckle noise from around the
focused spot in order to obtain a clean point laser beam to illuminate the sample.
This pinhole spatial filter (illustrated around pinhole D1 in Figure 9.29) is located
at A in Figure 9.28. The clean laser beam is reflected by a beamsplitter and goes
through an objective lens to illuminate the sample.
311
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9.3 Raman Microscopy
9 Vibrational Spectroscopy for Molecular Analysis
Eyepiece
Coupling optics
D2
Removable mirror
Pinhole spatial filter
Pinhole spatial filter spectrometer
Entrance slit
Beam splitter
Filter
D1
Microscope objective
Sample
Figure 9.29 Optical diagram of a Raman microscope. A pinhole spatial filter consists of
a pinhole confocal diaphragm (D1 and D2 ). (Reproduced with permission from Ref. [4]. ©
1996 Elsevier B.V.)
The Raman-scattered light is collected by a wide-aperture objective lens and
focused in an adjustable pinhole D2 placed in the image plane of the microscope.
The second pinhole spatial filter around D2 is located at B in Figure 9.28. The
pinholes D1 and D2 are called confocal diaphragms because they are in exact optical
conjugation positions with respect to the point source in the object plane (the sample
surface), similar to the confocal aperture in confocal microscope introduced in
Chapter 1. This confocal arrangement ensures that only light originating from the
microscopic area of the sample is transmitted to the spectral analyzer and detector.
These two pinhole spatial filters are important for illumination and Raman light
collection. They multiply and increase spatial resolution by eliminating stray light
coming from the out-of-focus region of the sample. By adjusting the pinhole
diaphragm D2 , the spatial resolution of the sample can reach 1 μm when a 100×
objective lens is used.
9.3.1.3 Prefilters
The scattered light from the microscope must be passed through special filters
before reaching the spectral analyzer in order to remove elastically scattered light.
The Raman light cannot be seen without the filters, because the elastically scattered
light has much higher intensity than the inelastically scattered Raman light. The
filter should ideally have a ‘‘notch’’ feature, as shown in Figure 9.30. The notch
is zero transmission in a narrow wave number range centered on a exciting laser
wave number. As illustrated in Figure 9.28 two holographic filters used in the
Raman microscope serve such a purpose.
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312
1
T
0
V0
Wave number (cm–1)
V
Figure 9.30 Spectral response of an ideal notch prefilter in micro-Raman spectroscopy to
remove the elastically scattered light with wave number vo . (Reproduced with permission
from Ref. [4]. © 1996 Elsevier B.V.)
9.3.1.4 Diffraction Grating
The key component of the spectral analyzer in the Raman microscope is the
diffraction grating. It disperses Raman-scattered light according to its wave numbers. The surface of the diffraction grating contains fine parallel grooves that
are equally spaced, as illustrated in Figure 9.31. When Raman scattered light is
incident on the diffraction grating, the grating disperses the light by diffracting it
in a discrete direction. The light dispersion is based on Bragg’s Law of diffraction
angle and incident wavelength. The diffraction grating plays a role similar to that
of the equispaced atomic planes in crystals. It diffracts the different wavelengths
in discrete angles (Figure 9.31). One diffraction grating can cover a range of 1000
wave numbers. For a Raman spectrum with a range of 400–4000 cm−1 , in order to
A
Substrate
B
I
D
A’
B’
a sin I
a sin D
Figure 9.31 Principle of optical grating diffraction.
Substrate normal
a
313
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9.3 Raman Microscopy
9 Vibrational Spectroscopy for Molecular Analysis
record the spectrum in the whole range, the grating should change its angle with
incident Raman scattered light. For a modern Raman microscope, the diffraction
grating can continuously rotate with respect to the incident Raman scattered light
and separate the Raman scattering wave numbers smoothly. The diffraction grating
can provide spectral resolution of 1 cm−1 .
Figure 9.31 illustrates the working principles of a diffraction grating. When light
rays A and B are incident on the grooves of the grating at angle I with respect to the
grating substrate normal, they will be reflected by the grooved surfaces as reflected
rays A and B at angle D with respect to the grating substrate normal. The path
difference between A and B is calculated
a sin I + a sin D
a is the distance between grooves. Constructive interference occurs when the
following condition is satisfied.
a(sin I + sin D) = mλ
(9.16)
m is an integer representing the order of diffraction. This basic grating equation
is similar to Bragg’s Law (Eq. (2.3)). Incident rays with different wavelengths are
reflected at different angles (are dispersed) according to the grating equation.
9.3.1.5 Detector
The Raman scattered light separated according to wavelength is recorded by a detector that is made from photoelectric materials. The detector converts photon signals
to electric signals. The detector for Raman scattered light is often multichannel and
solid state. The charged-coupled device (CCD) is the most commonly used detector.
A CCD is a silicon-based semiconductor arranged as an array of photosensitive
elements. A one-dimensional array of a CCD can detect and record light intensity of
discrete wavelengths separated by the diffraction grating. The Raman shift (mainly
Stokes scattering) is calculated and plotted versus wave number in the Raman
spectrum by computer processing.
9.3.2
Fluorescence Problem
Colored samples or impurities in polymer samples may absorb laser radiation and
re-emit it as fluorescence. The intensity of fluorescence can be as much as 104
times higher than that of Raman scattered light. The fluorescence problem is the
major drawback of using Raman spectroscopy. Thus, a Raman spectrum can be
completely masked by fluorescence. Three main methods can be used to minimize
fluorescence:
1)
Irradiate the sample with high-power laser beams for a prolonged time to
bleach out the impurity fluorescence.
2) Change the wavelength of laser excitation to a longer wavelength (nearinfrared). The chance of fluorescence is reduced because the excitation energy
of the laser beam is lower.
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314
3)
Use a pulsed laser source to discriminate against fluorescence because the
lifetime of Raman scattering (1012 to 1010 s) is much shorter than that of
fluorescence (10−9 to 10−7 s). Thus, an electron gate can be used to preferentially
measure the Raman signals.
Using a long-wavelength laser, however, generates a problem of Raman intensity
reduction, because the light intensity decreases with wavelength exponentially. A
Fourier transform type of Raman spectroscopy (FT-Raman) has been developed
that can solve fluorescence problems, particularly in conjunction with using a
longer wavelength. FT-Raman uses a Nd–YAG (yttrium aluminum garnet) laser
source, which generates excitation of IR wavelength (1064 nm) that does not cause
fluorescence in samples. Furthermore, the FT-Raman instrument collects the
Raman signal using the Michelson interferometer, which can accommodate large
beams. A larger beam can partially compensate for the loss of using a longer
wavelength. However, FT-Raman is not useful in Raman microscopy in which the
pinhole diaphragm has to be used to ensure spatial resolution.
9.3.3
Raman Imaging
Raman imaging is a technique to obtain spatial distribution of specific molecules
in a sample. It is similar to element mapping in X-ray, electron, and secondary
ion mass spectroscopy. The working principle is to record the specific Raman peak
that represents the specific component in the sample, as schematically shown in
Figure 9.32. Although it can be done with Raman microscopy, Raman imaging is
more difficult than other mapping techniques because the Raman scattered light
is inherently weak.
Raman imaging can be either obtained by a scanning or a direct-imaging method
in the Raman microscope. The scanning method requires a scanning mechanism
of a focused laser beam to generate a raster area in the sample, similar to scanning
electron microscope (SEM) imaging. The scanning method is often not favorable
because it is too time consuming. Unlike for SEM imaging, the intensity of Raman
scattered light is so low that the dwell time of the laser bean on each pixel should
be long in order to obtain a satisfactory two-dimensional image.
The direct-imaging method is rather simple, obtaining a complete twodimensional image for a chosen wave number, which represents a molecule,
by illuminating a whole area to be analyzed. The entire sample can be done by
defocusing the laser beam. Simple defocusing of the laser beam, however, will
generate uneven distribution of laser intensity as a Gaussian distribution with a
maximum at the beam center and very low intensity near the beam edge. A special
optical arrangement of the objective and condenser lenses in a Raman microscope
can be used to eliminate this problem.
A Raman image of a specific molecule is obtained by mapping its unique
wave number of Raman scattering. Thus, only the scattered light with a wave
number should be recorded by a two-dimensional detector. Raman wave number
selection can be readily performed by the diffraction grating, which serves as a
315
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9.3 Raman Microscopy
9 Vibrational Spectroscopy for Molecular Analysis
Rayleigh liine
Scattered intensity
(arbitrary units)
A
B
C
ν0
Δν (cm–1)
A
C
B
B
C
Conventional
image
Raman images
Figure 9.32 Principle of Raman imaging. The spectra of A, B, C represent those of substrate, molecule B and molecule C, respectively. (Reproduced with permission from Ref. [4].
© 1996 Elsevier B.V.)
wave number filter. Good spatial resolution images of a whole illuminated area can
be obtained by properly coupling the image plane of the objective to the surface
of diffraction grating. A high-quality Raman image also requires good spectral
resolution (narrow range of wave numbers). To achieve both spatial and spectral
resolution, more complicated filtering and optical systems are needed.
Figure 9.33 shows an example of Raman imaging with a direct-image method.
The image of the epoxy film reveals the rubber particles in the epoxy matrix. The
rubber exhibiting a Raman scattering at 1665 cm−1 generates the image contrast.
The rubber particles can effectively increase the toughness of the epoxy.
9.3.4
Applications
Raman spectroscopy is attractive as an examination technique for ceramic and
polymeric materials because it can simply examine them by illuminating their
surfaces regardless of sample thickness and form. Raman microscopy is even more
attractive because it can examine a microscopic area with diameters in the order
of 1 μm. Raman microscopy is increasingly used for materials characterization,
including:
• phase identification of polymorphic solids;
• polymer identification;
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316
5 μm
Figure 9.33 Raman image of rubber particles in epoxy film at 1665 cm−1 . (Reproduced
with permission from Ref. [4]. © 1996 Elsevier B.V.)
• composition determination;
• determination of residual strain; and
• determination of crystallographic orientation.
9.3.4.1 Phase Identification
Raman microscopy is able to determine phases for polymorphic solids at the microscopic level. This is its advantage over conventional X-ray diffraction spectrometry
in which the sample volume cannot be too small. Phase identification with Raman
spectroscopy uses the characteristic vibration band(s) associated with a certain
phase in a solid. For example, Table 9.2 lists characteristic vibration bands in Raman
spectroscopy in several polymorphic solids. This feature of Raman spectroscopy can
be further demonstrated using carbon as an example. Figure 9.34 shows four types
of carbon spectra that represent highly oriented graphite, polycrystalline graphite,
amorphous carbon, and diamond-like carbon. Significant differences appear
in Raman spectra for graphite and diamond because carbon atoms are bonded
with sp2 -type orbitals in graphite, while they are bonded in sp3 -type orbitals in
diamond.
Table 9.2
Phase identification with Raman microscopy.
Polymorphic materials
Phase 1
Bands (cm−1 )
Phase 2
Bands (cm−1 )
Si3 N4
BN
ZrO2
Carbon
α
Cubic
Monoclinic
Diamond
262, 365, 514, 670, 850
1055
181, 192
1332
β
Hexagonal
Tetragonal
Graphite
185, 210, 230
1367
148, 264
1580
317
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9.3 Raman Microscopy
9 Vibrational Spectroscopy for Molecular Analysis
(a) (b)
1700
1600
(d)
(c)
1500
1400
1300
1200
Wave number (cm−1)
Figure 9.34 Characteristic spectra of carbon in different structures: (a) highly oriented
graphite; (b) polycrystalline graphite; (c) amorphous carbon; and (d) diamond-like carbon.
(Reproduced with permission from Ref. [4]. © 1996 Elsevier B.V.)
Raman intensity (arbitrary units)
12345
Layer 1 and 5
(polyester)
Layer 2 and 4
(polyethylene)
Layer 3
(paper)
400
600
800
1000
1200
Raman shift
1400
1600
1800
(cm−1)
Figure 9.35 Raman spectra of a laminated polymer film obtained with excitation of a 785nm laser. (Reproduced from Ref. [8]. © 1999 Blackwell Publishing.)
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318
9.3.4.2 Polymer Identification
Raman microscopy is able to identify the different types of polymers even though
they all contain C, H, and O. For example, Figure 9.35 shows the Raman spectra of a
laminated polymer film. Individual layers can be identified with Raman microscopy
by focusing the laser beam on each of the layers in the cross section of the laminated
sample. The Raman spectra reveal the laminated sample is composed of polyester,
polyethylene, and a layer of paper.
Raman spectroscopy is sensitive to polymer conformation. For example, a
polymer blend of polybutadiene–polystyrene in which polybutadiene is used to
increase toughness of the polystyrene can be examined by Raman microscopy to
identify its heterogeneity. Polybutadiene has three isomer conformations (cis-1,4,
trans-1,4, and syndiotactic-1,2). These three types of isomers can be identified
from C=C stretching modes, as shown in Figure 9.36. The Raman spectra of the
copolymer indicate the difference in amounts of isomer types at the edge and the
center of the polybutadiene–polystyrene sample. The relative amounts of these
isomer types affect the mechanical properties of the copolymer.
9.3.4.3 Composition Determination
Raman microscopy has been used to monitor the amount of chemical elements
present in, or added to, a solid. For example, Figure 9.37 shows that the graphite
spectrum changes according to the number of molecules intercalated into its
1665 (trans)
1655 (1, 2)
1650 (cis)
(a)
(b)
ν (cm−1)
Figure 9.36 Raman spectra of
polybutadiene–polystyrene copolymer in the
C=C stretching region showing three distinct bands of polybutadiene isomers: cis-1,4
at 1650 cm−1 , trans-1,4 at 1665 cm−1 , and
syndiotactic-1,2 at 1655 cm−1 : (a) spectrum
from the center of the sample and (b) spectrum from the edge of sample. (Reproduced with permission from Ref. [4]. © 1996
Elsevier B.V.)
319
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9.3 Raman Microscopy
9 Vibrational Spectroscopy for Molecular Analysis
1617
E2g2
Stage 2
Intercalate
layer
Stage 2 GIC
1609
Graphate
layer
1586
Stage 3
1608
1586
Stage 4
Stage 3 GIC
1583
Stage 5
1606
Stage 4 GIC
Stage 5 GIC
1582
E02g2
Highly oriented pyrolytic graphite
(HOPG)
1400
1500
1600
1700
1800
Wavenumber / cm−1
Figure 9.37 Raman spectra of graphite and graphite intercalation compounds (GICs) with
FeCl3 . A lower stage number indicates a higher degree of intercalation.
layered crystal structure. Molecular intercalation into gaps between the (0001)
planes of graphite changes the bonding strength between the planes, which in turn
changes the vibrational frequency in the graphite. The degrees of intercalation are
represented by the stage number, which indicates intercalation occurs in every stage
number of crystallographic planes; lower stage numbers mean higher degrees of
intercalation. The graphite spectrum is highly sensitive to the stage number of
intercalated graphite, as shown in Figure 9.37.
Raman microscopy has also been used to identify the composition variation of
Si1−x Gex semiconductor materials. Figure 9.38 shows the Raman spectrum of a
Si0.7 Ge0.3 film on Si substrate. The vibrations of Si–Si, Si–Ge, and Ge–Ge bonding
in the film generate three distinct Raman peaks. Note the Raman shift of Si–Si
vibration in Si1−x Gex is different from that of Si–Si in pure Si. The composition
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320
350
Intensity (a.u.)
300
121 nm
x = 0.3
Si-Si
250
Si-Si
substrate
200
Si-Ge
150
Ge-Ge
100
200
250
350
300
400
450
500
550
Raman shift (cm−1)
Figure 9.38 Raman spectrum of a Si1−x Gex thin film with thickness of 121 nm on Si substrate, with argon laser (457.9 nm) excitation. (Reproduced from Ref. [8]. © 1999 Blackwell
Publishing.)
520
100 nm
Raman shift (cm−1)
65.5 nm
515
84 nm
876 nm
50 nm
704 nm
510
121 nm
505
500
0.0
0.0
0.2
0.3
X
Figure 9.39 Raman peak shift relationship with the composition change in Si1−x Gex thin
film. The plot also indicates the film thickness effect on the relationship. (Reproduced from
Ref. [8]. © 1999 Blackwell Publishing.)
variation of Si1−x Gex is related to Raman peak positions in the spectrum. Figure
9.39 shows that the Raman shift position is linearly related to the amount of Ge
added in the Si.
9.3.4.4 Determination of Residual Strain
Residual strain in a solid can also be determined by the shift of Raman bands
because strain changes the length of a bond between atoms and vibrational
frequency is exponentially affected by the bond length. For example, compressive
321
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9.3 Raman Microscopy
9 Vibrational Spectroscopy for Molecular Analysis
bulk
Intensity (arb. units)
SOS
540
530
520
510
500
Frequency (cm−1)
Figure 9.40 Comparison of Raman peak position in bulk Si and a Si film on sapphire
(SOS). (Reproduced from Ref. [8]. © 1999 Blackwell Publishing.)
strain in a microscopic area of a sample will reduce the bond length, and in turn,
increase the corresponding vibrational frequency. Figure 9.39 clearly indicates the
residual strain effect on Raman shift. A thin Si–Ge film on Si substrate contains
residual stress because the lattice parameter of Ge is different from that of Si. The
larger lattice parameter of Ge (0.566 nm) than that of Si (0.543 nm) generates biaxial
compression in the film. The residual compression strain alters the relationship
between the Raman shift and Ge content, as indicated by a solid line, compared with
the dotted line that represents the relationship when residual strain is not present
in the Si–Ge film. In thicker films, the residual stress is relaxed by formation of
cracks. Thus, the relation between Raman shift and Ge content is closer to the
dotted line.
Figure 9.40 shows another example of residual strain effects on the Raman
spectrum. The Si stretching vibration changes its frequency when Si is in the form
of a thin film on sapphire. We can compare the Raman band positions between
the strain-free sample and strained sample to evaluate the bond-length change,
which can be converted to residual strain. The residual strain is commonly elastic
in nature. Thus, the residual stress in materials can be determined with the linear
elastic relationship between strain and stress.
9.3.4.5 Determination of Crystallographic Orientation
Crystallographic orientation in a sample area can also be determined by measuring
the intensity change of Raman scattered light in different polarization directions.
The method of crystal-orientation determination requires extensive theoretical
treatment, which is beyond the scope of this book. However, its concept can be
understood from the following description. When polarized light is scattered by a
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322
crystallographic plane of a sample, the polarization of light will be changed. The
degree of change will depend on the angle between the polarization direction of
incident light and direction of the crystallographic plane, and the angle between the
polarization direction of scattered light and direction of the crystallographic plane.
If we measure the scattered-light intensity change with polarization direction using
an analyzer, the direction of the crystallographic plane at the examined sample area
can be determined.
9.4
Interpretation of Vibrational Spectra
Theoretical interpretation of molecular vibration spectra is not a simple task.
It requires knowledge of symmetry and mathematical group theory to assign
all the vibration bands in a spectrum precisely. For applications of vibrational
spectroscopy to materials characterization, we can still interpret the vibrational
spectra with relatively simple methods without extensive theoretical background
knowledge as follows.
9.4.1
Qualitative Methods
A simple way to qualitatively interpret vibrational spectra is the ‘‘fingerprint’’
method of identifying materials. The fingerprint method includes spectrum comparison with a reference, and identification of characteristic bands in spectra.
9.4.1.1 Spectrum Comparison
Spectrum comparison is the simplest method to interpret a vibration spectrum.
We do not need to have much theoretical knowledge of spectrum interpretation
for doing so. A sample can be identified if its spectrum matches a reference in
both band positions and intensities in the whole spectrum range. There is no need
to assign vibration bands in a spectrum in spectrum comparison. Comparison of
sample and reference spectra should satisfy the following conditions; otherwise the
spectra are not comparable:
• both sample and reference spectra must be in the same physical state (for
example, either both are liquid or solid) and
• both sample and reference must be measured using the same techniques (for
example, both are dispersed with KBr for FTIR measurement).
Certain bands of solid samples do not appear in liquid and gaseous samples.
Physical and/or chemical interactions of the sample with a dispersing matrix can
alter the spectrum and make comparison impossible.
Typical applications of spectrum comparison include verifying whether synthetic
materials are identical to their natural counterparts, and determining the stability
of materials over a period of time or in certain environments. For spectrum
323
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9.4 Interpretation of Vibrational Spectra
9 Vibrational Spectroscopy for Molecular Analysis
1
2
3
4
1000 cm−1800
600
400
200
ν
Figure 9.41 Comparison of Raman spectra of AHMo5 O16 (H2 O)H2 Om : A = (1) NH4 + ;
(2) K+ ; (3) Na+ ; and (4) compound spectrum in aqueous solutions. (Reproduced from
Ref. [1].)
comparison, a region of spectrum below 1200 cm−1 is of importance, often called
the ‘‘fingerprint region.’’ The reason is that the region of relatively low wave number
shows the vibrational bands involving large parts of molecules and crystals. The
band positions and intensities in such a region are more sensitive to minor
chemical variations. For example, exchange of the A+ ion species in compounds of
AHMo5 O16 (H2 O)H2 Om , can be detected by comparing fingerprint regions in the
Raman spectra of the compounds, as shown in Figure 9.41.
9.4.1.2 Identifying Characteristic Bands
Vibrational frequencies of some atom groups are quite independent even if they are
parts of larger molecules and crystals. Such vibration bands serve as characteristic
bands for atom groups. A characteristic band for an atom group should satisfy the
following conditions:
• the band occurs in all spectra of materials containing the atom group and
• the band is absent when materials do not contain the atom group.
For example, compounds containing the –CH=CH2 group exhibit a band near
1650 cm−1 ; and compounds containing O–H stretching vibration exhibit a band
near 3500 cm−1 in their IR spectra.
It is helpful to have basic knowledge of the relationship between vibrational
frequencies and bond strength and atomic masses. We may use the relationship
in understanding and assigning positions of characteristic bands in spectra. This
relationship can be illustrated with the simplest vibration of a diatomic model.
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324
Classical mechanics shows the vibrational frequency relationship
νvib ∝ f (m1 + m2 )/(m1 m2 )
(9.17)
f is the bond strength of atom 1 with mass m1 and atom 2 with mass m2 . This
equation indicates that vibrational frequency increases with the bond strength
and decreases with atomic mass. Thus, it is understandable that the following
relationships hold for vibration frequency increases.
ν(C ≡ C) > ν(C = C) > ν(C—C)
(9.18)
ν(C—H) > ν(C—O) > ν(C—Cl)
(9.19)
Also,
Figure 9.42 illustrates approximate distributions of some diatomic stretching
vibrational bands in spectra. It clearly demonstrates the relationship between wave
number (∝ ν vib ) and characteristics of bonds. Characteristic bands in Figure 9.42
show ranges instead of exact wave numbers. This phenomenon reflects the fact
that the vibrational frequencies also depend on neighboring atoms in materials,
even though the frequencies are mainly determined by bond strength and atomic
masses.
In general, the analysis method based on identifying characteristic bands is
applicable to polymers and ceramics. Theoretically, vibrational spectra of such
materials are generally complicated in nature. Their complex nature arises from
several aspects: the presence of new bonds coupling repeated units, the large
number of vibration bands (3N − 6) due to a large number of atoms (N) in a
C–D
C–H
C–F
C–I
C–H
Single
bond
C–CI
C–Br
C–O
C–C
C–N
S–H
X–H
O–H
P–H
N–H
S–H
C=C
C≡N
x=y or x≡y
Double
or trible
C ≡C
4 000
C–S
C=N
C=O
3 000
2 000
C=S
P=O
S=O
1 000
0
cm−1
Figure 9.42 Positions of characteristic bands in vibrational spectra for some diatomic
stretching vibrations. (Reproduced from Ref. [1].)
325
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9.4 Interpretation of Vibrational Spectra
9 Vibrational Spectroscopy for Molecular Analysis
polymer molecule, and vibration coupling of crystal lattices. Practically, vibration
spectra of polymers and ceramics are often considered as a summation of the
spectra of individual repeat units or functional groups, with slight modifications
due to the presence of new bond coupling between the repeated units. The
characteristic bands can still be identified; however, the bands may be broadened
or slightly shifted. Relatively few extra vibration bands from molecular chain and
crystal structures are observed in spectra of polymers and ceramics.
We may use the characteristic bands to distinguish compounds that include or
are composed of similar ion groups. For example, hydroxyapatite [Ca5 (PO4 )3 OH]
can be distinguished from other compounds of calcium phosphates, for example,
such as tricalcium phosphate [Ca3 (PO4 )2 ], in Raman spectroscopy by its hydroxyl
band in its IR or Raman spectrum. Raman microscopy (Figure 9.43) demonstrates
that a calcium phosphate coating layer produced by plasma sprayed on a titanium
substrate exhibits compositional changes in the coating layer. The relative amount
of hydroxyapatite in different depths of the coating layer of calcium phosphate
can be estimated by comparing the intensity of the O–H stretching band at about
3600 cm−1 in different locations of a coating layer: near the surface, in the middle
of layer and close to the substrate interface.
On the other hand, limitations of using characteristic bands should not be
ignored. For example, some characteristic bands may overlap each other. The
vibrational bands for O–H and N–H stretching occur in the same region in the
spectra, as shown in Figure 9.42. Also, certain factors can shift or eliminate
characteristic bands. Commonly, characteristic bands are distinct for organic
materials, but may not be for inorganic materials. One reason is strong vibrational
coupling in inorganic materials. Such coupling occurs when bond strength and
atomic masses vary slightly through inorganic molecules. For example, an isolated
Coating
3578.8
Titanium substrate
Intensity
c
b
a
3500
3550
3600
3650
3700
Wave number (cm−1)
Figure 9.43 Raman spectra of plasma-sprayed calcium phosphate coating showing the difference in hydroxyapatite content by comparing intensity of the OH stretching band at: (a)
near substrate; (b) in the middle; and (c) near the surface of the coating layer.
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326
C=O stretching band is located at 1620–1830 cm−1 . For CO2 with two C=O bonds
sharing one carbon atom, the stretching vibrations of C=O become one symmetric
and one antisymmetric vibration (Figure 9.8). The two distinctive vibrational bands
are located at 1345 and 2349 cm−1 , respectively.
9.4.1.3 Band Intensities
Interpreting the intensities of vibrational bands in a vibrational spectrum is not
straightforward. The band intensity is not simply proportional to the number
of atoms involved with such specific vibration. The intensity varies with types
of bonds and types of spectroscopy, either IR or Raman. The intensity of an IR
absorption band is proportional to the square of its change in dipole moment during
vibration.
2
∂μ
(9.20)
I(IR) ∝
∂q
But the intensity of a Raman shift is proportional to the square of its change in
polarizability during vibration.
2
∂α
(9.21)
I(Raman) ∝
∂q
In practice, some simple rules are useful to estimate the band intensities:
• polar bonds yield intense IR but weak Raman bands;
• weak polar or nonpolar bonds yield intense Raman but weak IR bands; and
• intensity increases with number of identical structural elements in a
molecule.
To illustrate, Table 9.3 lists several structural elements of molecules and their
intensity in IR and Raman bands. The intensity of a vibration band is often
more complicated than is indicated in this table. For example, Table 9.3 suggests
that unsaturated bonds (= and ≡) exhibit higher band intensities in Raman
than in IR spectra. However, this is not always true. For example, Figure 9.44
shows a comparison of IR and Raman spectra of a copolymer sample, EVA
(ethylene–vinyl acetate). The C=O band shows high intensity in the IR spectrum,
not the Raman spectrum. More detailed information about band intensities,
including band contours and the effects of vibration symmetry on intensity, can be
found in the references listed at the end of this chapter.
9.4.2
Quantitative Methods
9.4.2.1 Quantitative Analysis of Infrared Spectra
The concentration of certain components in a multicomponent sample can be
determined by quantitative analysis of its vibrational spectrum. Similar to quantitative analysis of X-ray diffraction spectra, the concentration of a component
can be evaluated from the intensities of its vibration bands. For an IR spectrum,
327
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9.4 Interpretation of Vibrational Spectra
9 Vibrational Spectroscopy for Molecular Analysis
Table 9.3
Intensity estimations of IR and Raman bands for certain structure elements.
Systema
Structure element
Intensityb
Vibration
IR
X–Y
ν(C–C)
w
s
ν(C–X)
s
vs
ν(O–H)
ν(C=C)
s
w
w
s
ν(C=O)
s
s
C C
C X*
R O H
X=Y
C=C
C=O
C≡C
ν(C≡C)
w
s
O=C=O
ν s (YXY)
w–m
s
C
ν as (YXY)
s
w
X≡Y
Y–X–Y
Raman
C
X = heavy atom.
w = weak, m = medium, s = strong, vs = very strong.
Data reproduced from Ref. [1].
a
Raman intensity/IR transmission
b
600
IR spectrum (layer (a))
Raman spectrum
(layer (a))
C-C=O
C=O
800
1000
1200
1400
Wave number (cm−1)
1600
Figure 9.44 Comparison of IR and Raman spectra of copolymer ethylene–vinyl acetate (EVA). EVA is distinguished by the C=C bands. (Reproduced from Ref. [8]. © 1999
Blackwell Publishing.)
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328
concentration is proportional to absorbance (A) according to the absorption law,
also called Beer’s Law
A = − log T = log
Io
= alC
I
(9.22)
%T
a is the absorptivity that is a constant at a particular wave number and l is the sample
thickness or the path length of radiation in the sample. I and Io are defined in Eq.
(9.14). The concentration (C) can be determined by measuring the magnitude of
absorbance from an IR spectrum, if a and l are known. These latter two parameters
can be obtained by using a calibration graph of A versus C if we have several
samples of known concentrations.
The absorbance A is commonly obtained by peak-height measurement in quantitative IR analysis. Figure 9.45 illustrates how to measure I and Io from a
conventional IR spectrum in which %T is plotted against the wave number. We
should note that the transmittance (T), cannot be directly used for quantitative
analysis. The figure shows a popular method for measuring Io using a baseline
method. The baseline is drawn tangentially to the spectrum at the wings of the
analytical band. The baseline intersection with a vertical line at the wave number
of band peak is used as Io .
We should know that the peak height is sensitive to instrument resolution. The
peak-area measurement under a vibration band shows much less instrumentation
dependence. The peak area represents the integrated intensity of the vibration band
and is proportional to the square of the change in dipole moment with respect to
the normal coordinate as Eq. (9.20).
For analysis of two-component materials, a ratio method can be used for
quantitative analysis based on Beer’s Law. For example, there is a mixture of two
components and two components have their own characteristic bands, which do
I
Io
ν
Figure 9.45 Baseline method for determining absorbance. (Reproduced with permission
from Ref. [2]. © 1990 Elsevier B.V.)
329
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9.4 Interpretation of Vibrational Spectra
9 Vibrational Spectroscopy for Molecular Analysis
not interfere with each other. Then, the ratio of their absorbance will be calculated.
A1
a l C
= 11 1
A2
a2 l 2 C2
(9.23)
The path lengths should be the same in the same sample. We can determine the
ratio of a1 : a2 using a standard sample in which C1 is known.
a1
1
A1
=
−1
(9.24)
a2
C1
A2
For analysis of multicomponent materials with overlapping vibration bands,
Beer’s Law can still be used because absorbances of components are additive.
Combining a and l as a single parameter k, the absorbance of components is
expressed.
A = k1 C1 + k2 C2 + k3 C3 + . . . kn Cn
(9.25)
There will be n number of equations and n × n number of k parameters for a
sample with n number of components. For example, a three-component system
should have the following expressions.
A1 = k11 C1 + k12 C2 + k13 C3
A2 = k21 C1 + k22 C2 + k23 C3
A3 = k31 C1 + k32 C2 + k33 C3
(9.26)
The best way to write a group of linear equations like Eq. (9.26) is to use the matrix
form.
A = KC
(9.27)
The concentrations of components should be resolved as C
C = PA
(9.28)
where P = K− 1 , the inverse of K matrix. This method is required to determine all
the k values in the K matrix for standard samples.
9.4.2.2 Quantitative Analysis of Raman Spectra
Raman spectroscopy is a scattering, not an absorption technique as FTIR. Thus,
the ratio method cannot be used to determine the amount of light scattered unless
an internal standard method is adopted. The internal standard method requires
adding a known amount of a known component to each unknown sample. This
known component should be chemically stable, not interact with other components
in the sample and also have a unique peak. Plotting the Raman intensity of known
component peaks versus known concentration in the sample, the proportional
factor of Raman intensity to concentration can be identified as the slope of the plot.
For the same experimental conditions, this proportional factor is used to determine
the concentration of an unknown component from its unique peak. Determining
relative contents of Si and Ge in Si–Ge thin films (Figures 9.38 and 9.39) is an
example of quantitative analysis of a Raman spectrum.
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330
Questions
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
Can we identify atoms or monatomic ions of materials using vibrational
spectroscopy? Why?
Can the vibration spectroscopic method be used to examine a metal sample?
Why?
Does a higher wave number band in an infrared spectrum mean higher
bond strength between atoms?
Determine the normal modes of planar molecule XY3 with a central symmetric configuration, where X is located at the center of the molecule.
Find out the normal modes of tetragonal molecule XY4 .
List the similarities of, and differences between, IR and Raman spectroscopy
in terms of working principles, spectra, and detectable vibration bands.
What is/are the advantage(s) of using an FTIR instead of a dispersive IR
spectrometer?
Determine which vibration mode of planer (CO3 )2− is not infrared active. Is
that mode Raman active? Why?
Are the vibration modes of H2 O shown in Figure 9.13 infrared active?
Why does transmission IR require samples to have thickness in the range
1–20 μm? How can we examine materials in bulk form?
Why is KBr used in FTIR system as supporting material in a beamsplitter
and sample holder?
Why does IR spectroscopy require radiation containing continuous wavelengths while Raman spectroscopy requires a monochromatic source?
Why does FTIR require a dry environment and also often cooling down to
the liquid nitrogen temperature?
What are the special requirements for a microscope in a Raman microscope
compared with a conventional light microscope?
Why does the fluorescence emission from a sample cause problems in
Raman spectroscopy?
Where is the ‘‘fingerprint region’’ in a vibration spectrum?
What kinds of vibrational bands are considered as characteristic bands?
References
1. Fadini, A. and Schnepel, F.-M. (1989)
4. Turrell, G. and Corset, J. (1996) Raman
Vibrational Spectroscopy, Methods and
Applications, Ellis Horwood, Chichester.
2. Colthup, N.B., Daly, L.H., and Wiberley,
S.E. (1990) Introduction to Infrared and
Raman Spectroscopy, 3rd edn, Academic
Press, San Diego, CA.
3. Hendra, P., Jones, P.C., and Warnes, G.
(1991) Fourier Transform Raman Spectroscopy, Instrumentation and Chemical
Applications, Ellis Horwood, Chichester.
Microscopy, Developments and Applications, Academic Press and Harcourt
Brace & Company, London.
5. Ferraro, J.R., Nakamoto, K., and Brown,
C.W. (2003) Introductory Raman Spectroscopy, 2nd edn, Academic Press, San
Diego, CA.
6. Smith, B.C. (1996) Fundamentals of
Fourier Transform Infrared Spectroscopy,
CRC Press, Boca Raton, FL.
331
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References
9 Vibrational Spectroscopy for Molecular Analysis
7. Jumecki, H.J. (1995) Practical Guide
to Infrared Microspectroscopy, Marcel
Dekker, New York.
8. Pelletier, M.J. (1999) Analytical Applications of Raman Spectroscopy, Blackwell
Science, Oxford.
Further Reading
Nakamoto, K. (1986) Infrared and Raman
Spectra of Inorganic and Coordination
Compounds, John Wiley & Sons, Inc.,
New York.
Mohan, J. (2000) Organic Spectroscopy, Principles and Applications, CRC Press, Boca
Raton, FL.
Chase, D.B. and Rabolt, J.F. (1994) Fourier
Transform Raman Spectroscopy, from Concept to Experiment, Academic Press, San
Diego, CA.
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332
10
Thermal Analysis
Thermal analysis (TA) is a group of analytical techniques that measure properties
or property changes of materials as a function of temperature. Changes in materials properties with temperature are considered as thermal events. The properties
that can change include dimension, mass, phase, and mechanical behavior. TA
methods are relatively simple because changing the temperature of a sample is
less complicated than probing a sample using high-energy X-ray, electron or ion
beams in techniques of spectroscopy. Many TA methods have been developed for
a variety of examination purposes. Table 10.1 lists commonly used TA techniques.
This chapter introduces the most commonly used TA techniques for materials
characterization: thermogravimetry (TG), differential thermal analysis (DTA), and
differential scanning calorimetry (DSC). TG is mainly used to examine the decomposition of materials by monitoring mass change with temperature. DTA and DSC
are widely used for examining the phase changes of materials.
10.1
Common Characteristics
10.1.1
Thermal Events
TA relies on material reactions to thermal energy flow in or out of solids. Such
reactions are referred to as thermal events. Possible thermal events of a solid can be
reviewed by increasing its temperature from absolute zero (0 K). At absolute zero,
a solid does not have any thermal energy, and it means that its atoms are static:
there is no vibration or rotation of atomic bonds. With increasing temperature,
thermal energy gains in the solid will increase vibrations and rotations of atomic
bonds. When the amplitudes of vibrations reach a certain level, the following
changes in the solid may occur if the solid is in an inert atmosphere: solid-phase
transformation, glass transition, melting, sublimation, and thermal decomposition.
Solid-phase transformation may occur for solids that have different equilibrium
crystalline phases in different temperature ranges. For example, pure iron changes
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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333
10 Thermal Analysis
Table 10.1
Commonly used thermal analysis techniques.
Technique
Abbreviation
Measurement
Thermogravimetry
Differential thermal analysis
Differential scanning calorimetry
Dilatometry
Thermomechanical analysis
Dynamic mechanical analysis
TG
DTA
DSC
—
TMA
DMA
Mass change
Temperature difference
Heat flow
Length or volume change
Deformation
Deformation
its crystal structure from body-centered cubic (BCC) to face-centered cubic (FCC)
when the temperature increases to 912 ◦ C. Glass transition occurs in noncrystalline
solids. With increasing temperature, a rigid noncrystalline solid in a glass phase
may change to a rubber-like solid. The glass transition is referred to as a second-order
phase transition. It is distinguishable from first-order phase transitions in the solid
state, which are phase transformations in crystalline solids. The glass transition
is an important property of polymeric materials. Melting is simply the phase
transformation from solid to liquid, and sublimation is the phase transformation
from solid to gas. Thermal decomposition is referred to as a change in a solid
containing more than one type of atom or molecule. With increasing temperature,
the bonding between atoms becomes so weak that certain constituents will be
released from the solid into the atmosphere and the remaining constituents will
form a new type of solid. For example, solid CaCO3 will decompose to form solid
CaO and gaseous CO2 over a certain temperature range.
Table 10.2 lists the thermal events that may occur when a solid (A) is heated in an
inert atmosphere. The heat flow between a solid and its surrounding atmosphere
at a certain temperature is indicated as the enthalpy change (H) in Table 10.2.
H quantifies the heat flowing into or out of a solid under constant pressure.
Commonly, thermal events occurring under a constant-pressure atmosphere are
analyzed in TA instruments.
Table 10.2
Thermal events during heating of a solid in an inert atmosphere.
Thermal event
Reaction
Heat flow ΔH
Mass change in solid
Solid phase
transformation
Glass transition
Melting
Sublimation
Thermal
decomposition
A (solid α) → A (solid β)
+ or −
No
A (glass) → A (rubber)
A (solid) → A (liquid)
A (solid) → A (gas)
A (solid) → B (solid) + C (gas)
No
+
+
+ or −
No
No
Yes
Yes
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334
10.1.1.1 Enthalpy Change
Enthalpy is the thermodynamic parameter that is useful for describing the thermal events
of a material under constant pressure, for example, 1 atm. We can understand the
meaning of enthalpy and enthalpy change by reviewing the first law of thermodynamics.
U = Q − W
(10.1)
The internal energy change U of a system is a sum of the heat flowing into it (Q) and
the work done by the system (−W). Heat is defined as the energy transfer between the
system and its surroundings due to their temperature difference. Work includes all types
of energy transfer other than heat. If we consider that the work is mechanical work of
volume change in the system under constant pressure, then the first law should be written
as follows
U = QP − PV
(10.2)
QP represents the heat required for internal energy change under constant pressure.
Enthalpy is defined as H.
H ≡ U + PV
(10.3)
Thus, under constant pressure, the enthalpy change will be written
H = U + PV
or
U = H − PV
(10.4)
Comparing Eqs. (10.2) and (10.4), we can conclude the following.
H ≡ QP
(10.5)
Thus, the heat flowing in or out of a system under constant pressure is equal to its
enthalpy change. In the rest of Chapter 10, the heat flow under constant pressure will be
measured as the enthalpy change, H. Quite often we simply refer to H as ‘‘enthalpy,’’
not ‘‘enthalpy change,’’ although the latter is technically correct.
10.1.2
Instrumentation
All TA techniques have certain features in common in their instrumentation: a
furnace in which a sample is heated (or cooled) with a controllable environment,
and a transducer by which the property changes in materials are monitored.
Figure 10.1 illustrates general TA instrumentation. The sample is analyzed under
a designed temperature profile. The temperature profile may take several forms
such as a constant heating rate, a modulated heating rate (for example, a sinusoidal
heating curve), or even an isothermal profile. The measurements are displayed as
TA curves. The features of the curves (peaks, discontinuities, and slope changes)
are related to thermal events.
335
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10.1 Common Characteristics
10 Thermal Analysis
Transducer
Amplifier
Evolved
gas analysis
Y
Computer
- data
capture
- control
X
Sample
Furnace
Carrier
gas
Programmer
Display
Y
X
Figure 10.1 General instrumentation for thermal analysis. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 2001 Springer Science.)
10.1.3
Experimental Parameters
TA results can be significantly affected by experimental parameters such as sample
dimension and mass, heating (or cooling) rates, atmosphere surrounding the
sample, and even thermal and mechanical history of the sample. Reproducible
results of a chemical species may not be obtained when the instrumental and
experimental parameters are not identical. The main reason for this is that TA
is highly sensitive to heat-transfer conditions and to accuracy of temperature
measurements. The following considerations can help ensure reliable TA data.
Sample dimension and mass should be small. For most TA techniques, samples
in the form of a powder with sample mass less than 10 mg are preferred. Heat
transfer between the sample and atmosphere will be faster in such a sample than in
a lump; thus, thermal equilibrium is more likely to be achieved between sample and
atmosphere during analysis. Samples to be analyzed should have the same thermal
and mechanical history. Thermal events are affected by such history and different
results for the same chemical species are likely to be generated if the samples
have different histories. The main reason for this is that thermal measurement is
affected by the internal energy of samples, and the internal energy can be changed
by thermal and mechanical processes.
The heating rate probably is the most important parameter to affect TA results. A
slow heating rate is often favorable in order to approach thermal equilibrium during
TA. A fast heating rate will generate a thermal lag between the heating source
and sample. The thermocouple for temperature measurement in a TA instrument
is rarely in direct contact with the sample. A fast heating rate can generate a
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336
temperature gradient surrounding the sample and errors in measurement of
sample temperature result.
The atmosphere surrounding the sample serves to transfer heat and supply or
remove gaseous reactants or products. Thus, its chemical nature and flow affect the
TA data. In most TA methods, we need an inert atmosphere to prevent the sample
from oxidation reactions. Maintaining a certain flow rate is important for TA
involving a gaseous product; for example, examination of thermal decomposition.
The flow will provide a stable partial pressure of products.
10.2
Differential Thermal Analysis and Differential Scanning Calorimetry
DTA and DSC are the most widely used TA techniques. Both techniques have
the same objective: to examine thermal events in a sample by heating or cooling
without mass exchange with its surroundings. The thermal events examined by
DTA and DSC include solid-phase transformation, glass transition, crystallization,
and melting. ‘‘Differential’’ emphasizes that analysis is based on differences
between sample material and a reference material in which the examined thermal
events do not occur.
10.2.1
Working Principles
10.2.1.1 Differential Thermal Analysis
A DTA instrument is designed to measure temperature differences between the
sample and reference, as illustrated in Figure 10.2. A sample and reference are
symmetrically placed in a furnace. The temperature difference between the sample
and reference are measured by two thermocouples: one is in contact with the
underside of the sample holder (also called the crucible), the other is in contact
with the underside of the reference holder. The reference should be made from a
material that satisfies the following conditions: it does not undergo thermal events
over the operation temperature range, does not react with any component in the
instrument, and has similar thermal conductivity and heat capacity to the sample
being examined.
The temperature difference between sample and reference (T) should be
zero when no thermal event occurs in the sample, because of similar thermal
conductivity and heat capacity between the sample and reference. When a thermal
event occurs in the sample, nonzero T will be generated. T will be negative if
the thermal event is endothermic (absorbing heat) or positive if the thermal even is
exothermic (releasing heat). An endothermic event makes the sample temperature
lower than the reference temperature that follows the heating program closely.
On the other hand, an exothermic event makes the sample temperature higher
than the reference temperature. A DTA curve will reveal thermal events over
a certain temperature range, as illustrated in Figure 10.3. The DTA curve is a
337
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
10 Thermal Analysis
Sample reference
Furnace
windings
Alumina gasflow tube
A
B
B A
V
Ts
V
TR
V
ΔT
Figure 10.2 Differential thermal analysis (DTA) instrumentation. VTs and VTr are the thermocouple voltages for measuring sample and reference temperatures, respectively. (Reproduced with permission from Ref. [2]. © 1993 Taylor & Francis Group Ltd.)
Endo.
Melting
ΔT
DTA curve
Glass transition
Exo.
Cold
crystallization
Measured sample
temperature
Time
Figure 10.3 DTA curve for a polymer sample under a constant heating rate. (Reproduced
with permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
plot of T versus reference temperature or heating time when heating rate is
constant.
10.2.1.2 Differential Scanning Calorimetry
A DSC instrument is designed to measure the heat-flow difference between sample
and reference. There are two widely used DSC systems: the heat flux DSC and the
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338
power-compensated DSC. The heat flux DSC is also called ‘‘quantitative DTA’’ because
it measures the temperature difference directly and then converts it to a heat-flow
difference, as illustrated in Figure 10.4a. This conversion is accomplished by an
algorithm in computer software installed in the system. The power-compensated
DSC directly measures the enthalpy change of a sample during a thermal event.
Its design is very different from DTA. In power-compensated DSC, there are two
separate chambers to contain the sample and reference. Each chamber has its own
individual heat element to control temperature (Figure 10.4b). The instrument
always maintains a thermal null state (T = 0). When a thermal event occurs in
the sample, the power to the heating element has to change in order to maintain
the sample temperature the same as that of the reference. An endothermic event
causes an increase in power to heat the sample; an exothermic event causes a
reduction in power to cool the sample. The amount of power change should equal
the energy of heat flow to compensate for the heat release or gain of the sample.
A DSC curve is illustrated in Figure 10.5 in which heat flow is plotted versus
temperature. The heat flow has a unit of energy per unit time per unit mass, usually
in units of W g−1 . Commonly, heat flow into a sample is indicated as an upward
feature of the DSC curve. This differs from a DTA curve in which an endothermic
event is indicated as a downward feature. The DSC curves are commonly recorded
over a temperature range by heating or cooling a sample with a constant rate,
similar to DTA curves.
Although DTA and DSC are similar in thermal event measurements and instrumentation, they are different in the following aspects. DTA is a qualitative technique
because measured temperature differences do not provide any quantitative data for
A
C
C
B
B
ΔT
dH/dt
ΔT = 0
dH/dt
(a)
(b)
Figure 10.4 Differential scanning calorimetry (DSC) instrumentation design: (a) heat flux
DSC and (b) power compensation DSC. A, furnace; B, separate heaters; and C, sample
and reference holders. (Reproduced with permission from Ref. [4]. © 1992 Royal Society of
Chemistry.)
339
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
DSC response
Endo
10 Thermal Analysis
Glass transition
Melting
Degradation
Oxidation
Crystallization
Tg
T
Figure 10.5 Schematic DSC curves for a polymeric sample. T g , glass-transition temperature. (Reproduced with kind permission of Springer Science and Business Media from Ref.
[1]. © 2001 Springer Science.)
energy. In contrast, DSC is a quantitative technique because measured heat flow
provides enthalpy changes in the sample during a thermal event. DTA can operate
over a wider temperature range than DSC. The DTA can reach a temperature of
greater than 1500 ◦ C, while the power-compensated DSC is restricted to a maximum temperature of about 750 ◦ C. This DTA feature is important for examining
materials with high melting temperature such as ceramics and some metals.
10.2.1.3 Temperature-Modulated Differential Scanning Calorimetry
In conventional DSC measurements, the enthalpy change of thermal events in the
sample is measured at a constant heating rate. This means the sample temperature
change with time as written as follows
T = To + βt
(10.6)
T o is the starting temperature, t is time, and β is the heating rate.
Temperature-modulated differential scanning calorimetry (TMDSC) is an advanced DSC technique in which the heating rate is modulated by superimposing
a cyclic heating rate on the constant rate; for example, a sinusoidal temperature
modulation is superimposed on the temperature profile
T = To + βt + B sin(ωt)
(10.7)
B is the amplitude of temperature modulation that is commonly in the range
of ±1 to ±10 K and ω = 2π p−1 , in which p is the modulation period that is
commonly in the range 10–100 s. Figure 10.6 illustrates a TMDSC heating profile.
The constant heating profile to the sample can provide total heat-flow information,
while the sinusoidal heating profile gives information corresponding to the rate
of temperature change. Raw TMDSC data are rather complex compared with
conventional DSC data. TMDSC data require deconvolution to generate standard
DSC curves, such as the one shown in Figure 10.5.
To understanding the applications of TMDSC, we need to know the heat-flow
features of DSC. At any moment of a DSC experiment, the heat flow can be
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340
13.44 K/min
Modulated temperature/K
383.5
383.0
382
0
381.3
381.8
Modulated heating rate
(K/min)
15
385
380.8
Constant heating rate
379
381
382
Temperature/K
−15
383
Figure 10.6 Schematic temperature modulated DSC (TMDSC) curves for a polymeric sample. (Reproduced with permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
expressed as a differential equation
dH
= CP β + f (T, t)
dt
(10.8)
CP is the sample heat capacity. The first term on the right-hand side of Eq. (10.8)
represents the heat flow of reversing thermal events and the second term represents
the heat flow of nonreversing thermal events. f (T,t) is also referred as to the kinetic
component of heat flow.
The main advantage of TMDSC is its ability to separate the reversing and
nonreversing thermal events. Reversing thermal events include glass transition and
fusion (melting). Nonreversing thermal events include oxidation, curing, relaxation,
and cold crystallization (glass–crystal transition below the melting temperature).
Separating the reversing and nonreversing heat-flow components, TMDSC
can distinguish overlapping thermal events. Figure 10.7 illustrates the example
of using TMDSC to examine a poly(ethylene terephthalate)–poly(acrylonitrile–
butadiene–styrene) (PET–ABS) polymer blend. Figure 10.7a shows conventional
DSC curves of the polymer blend. The first heating curve reveals the PET glass
transition at 340 K, the PET cold crystallization at 394 K, and PET fusion at 508 K
(not shown). The ABS glass transition at 379 K cannot be observed in the first
heating curve because it is overlapped with the PET cold crystallization peak. The
ABS glass transition can only be revealed by a second heating after the first heating
and cooling. However, TMDSC clearly shows both PET and ABS glass transitions
in its reversing curve (Figure 10.7b). The TMDSC nonreversing curve not only
reveals the PET cold crystallization, but also a relaxation in the polymer blend at
343 K, which cannot be seen in Figure 10.7a.
341
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
10 Thermal Analysis
First heat
−0.4
−0.6
Second heat
after 10 K/min cooling
Nonreversing
Heat flow / (mW)
−0.10
470
−0.02
Total
−0.04
−0.12
Reversing
PET Tg
−0.14
−0.06
ABS Tg
320
(b)
370
420
Temperature/K
Figure 10.7 DSC curves of poly(ethylene
terephthalate)–poly(acrylonitrile–butadienestyrene) (PET–ABS) blends: (a) conventional
DSC first and second heating curves with
heating and cooling rate of 10 K min−1 and
(b) temperature modulated DSC (TMDSC)
−0.04
−0.06
−0.08
Nonreversing heat flow / (mW)
370
420
Temperature/K
320
(a)
Reversing heat flow / (mW)
Heat flow / (W/g)
−0.2
470
first heating curves with β = 2 K min−1 ,
p = 60 s, and B = ±1 K. T g , glass-transition
temperature. (Reproduced with permission
from Ref. [3]. © 1999 John Wiley & Sons
Ltd.)
10.2.2
Experimental Aspects
10.2.2.1 Sample Requirements
Samples for DTA or DSC should be in the form of dense powders or small disks.
Film, sheets, and membranes are often cut into disks fitting into the sample pans.
Large shear forces during cutting samples should be avoided because the shear
force may induce plastic deformation in a sample and that can affect DTA and
DSC curves. Low-mass samples are also preferred because a low-mass sample
can quickly reach temperature equilibrium throughout its volume. A large-mass
sample will have undesirable internal temperature gradient and this will affect the
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342
accuracy of the curve. Commercial DSC instruments are able to measure phase
change in microgram samples. In practice, the lower limit of sample size relates
to the nature of the sample materials. For composites and polymer blends, large
sample size of about 10 mg may be required.
DTA is usually operated in a high-temperature range. Platinum and gold crucibles
are commonly used as sample and reference holders. DSC is usually operated in
a low-temperature range (<500 ◦ C), and thus aluminum pans are commonly used
as sample and reference holders. The pans often need to be sealed to avoid sample
mass change due to evaporation. A special press can be used to mechanically weld
a lid and a pan together.
Endothermic
10.2.2.2 Baseline Determination
Thermal-event measurement from a DTA or DSC curve relies on determining
the deviation of the experimental curve from the curve baseline as shown by a
DSC curve (Figure 10.5). There are two baselines: the instrument baseline (also
called the zero line) and the sample baseline, as illustrated in Figure 10.8. The
instrument baseline is the curve recorded without the sample over the instrument’s
operational temperature range. Ideally, the instrument baseline is a straight line
over a temperature range. In practice, however, the baseline may be curved and/or
display a high level of noise. For example, the instrument may be contaminated
with trace amounts of residue from a previous experiment. Decomposition or
sublimation of such a residue will distort the instrument baseline. The instrument
baseline will also be affected if the flow rate of purge gas in the instrument is
not constant or if the purge gas contains a large amount of water vapor. Thus,
we should always check the instrument baseline by first running the instrument
without a sample.
The sample baseline of an experimental curve, as illustrated in Figure 10.8, is the
line that connects the curve before and after a peak, as if no peak had developed.
Accuracy of enthalpy-change measurement relies on correctly constructing the
Sample baseline
Instrument baseline
Temperature
Figure 10.8
Illustration of sample baseline and instrument baseline.
343
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
10 Thermal Analysis
sample baseline from the curve. Construction of the sample baseline from the
measured curve may not be straightforward. Figure 10.9 shows examples of how
to construct a baseline using interpolation methods for various curve shapes.
The procedure of baseline subtraction is often done automatically as it can be
incorporated in the software provided with the instrument.
10.2.2.3 Effects of Scanning Rate
DTA and DSC experiments are commonly run through a temperature range with
a constant heating or cooling rate. This rate should be reported with the DTA and
DSC results for reasons that are described here. The rate of scanning through
a temperature range affects the thermal-event measurement. More specifically,
the scanning rate can change the curve shape and characteristic temperature
indicated in a curve. Figure 10.10 shows scanning-rate effects on the DSC curve
of PET. Figure 10.10a reveals that the peak area of PET melting increases with
increasing heating rate. Figure 10.10b reveals that the crystallization temperature
of PET decreases and peak width increases with increasing cooling rate. From
Figure 10.9 Examples of sample baseline interpolation for different types of differential
thermal analysis (DTA) and DSC curves. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 2001 Springer Science.)
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344
Endo.
dH/dt / (arbitrary units)
III
II
I
440
460
440
460
480
Temperature /K
500
II
I
Exo.
dH/dt / (arbitrary units)
540
500
III
400
(b)
520
480
Temperature /K
(a)
420
520
Figure 10.10 Scanning rate effects on DSC curves of a poly(ethylene terephthalate) (PET)
sample: (a) heating and (b) cooling. I, 10 K min−1 ; II, 20 K min−1 ; and III, 40 K min−1 . (Reproduced with permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
Figure 10.10, we note that the scanning rate effects are even more obvious in
cooling than in heating. The rate effects on the curves simply reflect the fact that
thermal events are kinetic processes. The processes of material change, such as
melting, require time for heat transfer and atom or molecule diffusion.
Increase of the scanning rate will result in an increase of the temperature
gradient in the sample and the instrument, thus making it difficult for the sample
to reach equilibrium. Although a slower rate can make a measurement more
accurate, a fast heating rate often makes thermal event peaks more obvious in the
curve. The scanning rate of DTA and DSC instruments commonly varies from
0.1 to 40 ◦ C min−1 . We also should note that the programmed scanning rate may
not represent the true rate of sample heating or cooling, because of the possible
temperature gradient between sample and thermocouple. Scanning-rate effects are
difficult to eliminate, particularly for polymeric samples. Thus, the scanning rate
should be reported with the DTA and DSC results.
10.2.3
Measurement of Temperature and Enthalpy Change
10.2.3.1 Transition Temperatures
Measuring transition temperatures is the primary task of DTA and DSC. The
common transitions are melting, crystallization, and glass transition. Figure 10.11
345
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
Endothermic exothermic
10 Thermal Analysis
Tg
Tm
Tc
400
600
800
Temperature (°C)
1000
1200
Figure 10.11 DTA curve of glass–ceramic sample (Li2 O–Al2 O3 –6SiO2 ). Temperatures of
glass transition (T g ), crystallization (T c ), and melting (T m ) are determined from the curve.
(Reproduced with permission from Ref. [2]. © 1993 Taylor & Francis Group Ltd.)
demonstrates how to determine the temperatures of thermal events from a DTA
or a DSC curve. The DTA curve of a glass–ceramic sample shown in Figure 10.11
exhibits three thermal events during heating: glass transition, crystallization (or
devitrification), and melting. Melting and crystallization exhibit endothermic and
exothermic peaks, respectively. The glass transition exhibits only a change in the
slope of the curve. The glass-transition temperature (T g ) can be determined at the
point where the curve deviates from the linearity of the sample baseline. For DSC
curves that are not linear, T g should be determined at the temperature where the
curve deviates from the interpolated sample baseline, known as the onset temperature. T g can more reliably be defined as the intersection between two tangents to
the sample baselines before and after slope change when the point of the curve
deviating from the sample baseline is not certain, as shown in Figure 10.11. The
temperature of the first-order phase transition such as crystallization temperature
(T c ) and melting temperature (T m ) should be defined at the intersection of the
tangent to the maximum rising slope of the peak and the extrapolated sample
baseline. The method to define T m or T c can be understood by analyzing the
change of sample temperature during DTA scanning at a constant heating rate.
When a solid melts, the sample temperature (T s ) remains at the melting temperature while the reference temperature (T r ) continuously increases with heating.
Thus, T = (T s − T r ) starts to decrease, deviating from the baseline, until melting
is completed; thus, T reaches a minimum. The temperature of the melting
peak represents the temperature of melting completion. After that, the sample
temperature starts to increase to catch up with that of the reference during heating,
and the curve increases exponentially after melting is completed. The reason for
the exponential curve is that the sample temperature increases more rapidly at the
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346
Endothermic exothermic
Real
Ideal
Sample temperature
Figure 10.12 Comparison of real and ideal melting peaks in DTA curve at a constant heating rate.
moment right after melting completion but the temperature increase will gradually
slow when the temperature gradient between sample and surroundings decreases
with increasing sample temperature. Figure 10.12 illustrates an ideal DTA melting
peak when the x-axis is the true sample temperature. In a modern DTA instrument,
the sample temperature is not directly measured by a thermocouple junction in
contact with the sample, but in contact with the sample holder. Thus, the DTA peak
of melting has a shape as shown in Figure 10.12. In any case, the sharp turning
point from the baseline at the DTA curve, shown in Figure 10.12, should represent
the melting temperature. Comparing peaks in Figures 10.11 and 10.12, we can
conclude that the intersection point best represents the melting temperature. A
similar argument should apply to the T c determination, as well as to the T m and
T c determinations in DSC curves. The only difference is that the heat flow in DSC
replaces temperature change in DTA.
10.2.3.2 Measurement of Enthalpy Change
The enthalpy change of phase transformation can be directly measured from
the corresponding peak area of a DSC curve. The DSC is commonly plotted as
dH
per mass unit versus temperature. The total enthalpy change H should be
dt
proportional to the peak area (Ap )
H/mass = Kc Ap
(10.9)
where K c is a calibration factor that includes contributions from the experimental
conditions and the thermal conductivity of the system. We can obtain K c by
measuring the peak area of the standard samples, for which we know enthalpy
change, such as those listed in Table 10.3.
For the power-compensated DSC, K c is virtually independent of temperature. For
the heat flux DSC, K c becomes temperature dependent and has to be determined
at a temperature close to that of the peak to be measured. The Ap measurement
relies on interpolation of the sample baseline, as illustrated in Figure 10.9.
347
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
10 Thermal Analysis
Table 10.3
Standard materials for calibration.
Standard
Biphenyl
Benzil
Indium
Tin
Lead
Zinc
Aluminum
Melting temperature (◦ C)
Enthalpy change of melting (J g−1 )
68.93
94.85
156.61
231.92
327.47
419.53
660.33
120.6
110.6
28.71
60.55
23.00
108.6
401.3
10.2.3.3 Calibration of Temperature and Enthalpy Change
Besides the correction procedure in determining temperature and enthalpy change,
measurement accuracy relies on whether the instrument is well calibrated for the
given experimental conditions. Calibration should be done frequently with standard
materials. Standard materials are selected based on their well-characterized melting
temperatures and enthalpy changes of melting (also called latent heat). Table 10.3
lists commonly used standard materials for temperature and enthalpy calibration.
The listed materials cover the temperature range of about 69–660 ◦ C. It is important
to calibrate measurements of temperature and enthalpy change by selecting a
proper standard material for which the melting temperature falls within the
melting temperature range of the sample to be examined.
10.2.4
Applications
DTA and DSC are so similar in their working principles and in characteristics of
their curves that we often do not distinguish between these two techniques in their
applications for materials characterization. These two techniques are especially
useful in characterization of polymeric materials, as well as in characterization of
inorganic materials. Some typical applications of DTA and DSC are introduced in
this section.
10.2.4.1 Determination of Heat Capacity
The principle of heat capacity measurement is based on proportionality of the DSC
response to the heat capacity. By definition, the heat capacity of materials under
constant pressure is the following.
∂H
(10.10)
CP ≡
∂T P
Figure 10.13 illustrates the DSC curves for heat-capacity measurement.
Figure 10.13a shows an ideal instrument baseline and a DSC line with sample.
The displacement between the baseline and sample line (h) should be proportional
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348
Pan
+
sample
dH
dt
Displacement, h
Pan only
T
(a)
Standard
hs
dH
Sample
dt
h
Empty pan
(b)
T1
T
T
T2
Melting endotherm
dH
dt
Cp Liquid
Cp Solid
T
(c)
Figure 10.13 Heat-capacity measurement: (a) proportionality of heat capacity and DSC response; (b) two displacements required for heat capacity calculation; and (c) heat capacity
as a function of temperature. (Reproduced with kind permission of Springer Science and
Business Media from Ref. [1]. © 2001 Springer Science.)
to sample heat capacity.
h = BβCp
(10.11)
The proportional factors are determined by the heating rate (β) and by the calibration
factor (B). We can eliminate these factors if a DSC curve of a standard sample is
349
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
10 Thermal Analysis
recorded under exactly the same experimental conditions. Sapphire is commonly
used as the standard with known heat capacity. Figure 10.13b illustrates DSC curves
with an empty sample holder (pan), with a sample, and with a standard sample
recorded on the same chart. The heat capacity of the sample can be calculated
with the heat capacity of the standard (CPs ) and displacements measured from
Figure 10.13b.
hMs
(10.12)
CP = CPs
hs M
Ms and M are the mass of standard and sample, respectively, hs is the displacement
between the baseline and the standard line as marked in Figure 10.13b. The
displacements h and hs can be determined graphically.
Correct determination of the instrument baseline is important for accurate
heat-capacity measurement. The instrument baseline is not likely to be recorded
as a horizontal line in experiments. The displacements closed to T 1 and T 2 in
Figure 10.13b should not be used for measurement because the heating conditions
are not stable there. We should note that the measured heat capacity is more likely
to be a function of temperature, particularly when a thermal event occurs in the
measured temperature range (Figure 10.13c).
DSC response
Endo
10.2.4.2 Determination of Phase Transformation and Phase Diagrams
DTA and DSC curves are sensitive to the first-order transition, which exhibits
an enthalpy change. First-order transitions include melting and solid-state phase
transformations. The curve peaks of DTA and DSC readily reveal solid-state phase
transformations over a temperature range. Figure 10.14 shows an example of
phase-transformation detection. The DSC curve of carbon tetrachloride reveals
the solid-state transformation from a monoclinic to rhombohedral then cubic
Monoclinic
Rhombohedral
−50
−40
Cubic
−30
Liquid
−20
T (°C)
Figure 10.14 The DSC curve of carbon tetrachloride exhibits three solid-state phase transformations before melting. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 2001 Springer Science.)
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350
DSC or DTA response
exo
(cooling)
T
B
Mole fraction
A
Figure 10.15 Determining a binary phase diagram containing a eutectic reaction by DSC
or DTA. The dashed lines are of the phase diagram. (Reproduced with kind permission of
Springer Science and Business Media from Ref. [1]. © 2001 Springer Science.)
crystal structure during temperature change. Figure 10.14 also tells us that the
operating temperature of a DSC can be extended to the cryogenic range. A cooling
medium such as liquid nitrogen has to be used for measurement at cryogenic
temperatures. We can determine a phase diagram of a materials system by
determining transformation temperatures as a function of material composition.
Figure 10.15 shows an example of a binary phase diagram determination. A series
of cooling curves starting from the liquid state of materials are recorded. The
whole composition range of a binary system, from 100% component A to 100%
component B, is measured. In Figure 10.15, the liquidus lines (the curved lines in
Figure 10.15), and the eutectic temperature and composition are determined from
the transformation temperatures as revealed by DSC or DTA curves.
10.2.4.3 Applications to Polymers
Polymeric materials are more sensitive to temperature than metals and ceramics.
A large number of polymers exhibit physical and chemical property changes with
changes in temperature, as illustrated in Figure 10.5, a DSC curve of a quenched
crystalline polymer. Besides determining the temperatures of glass transition,
crystallization, and melting, we can also determine special properties of polymers
such as crystallinity, curing status, polymer content, and stability.
A large number of polymeric materials have both amorphous and crystalline
structures. The melting temperature is that of a crystalline solid to liquid transformation. We can estimate the crystallinity of polymer (X c ) by comparing its melting
H with that of its fully crystalline counterpart (H100 ).
Xc =
H
H100
(10.13)
The simple method based on Eq. (10.13), however, is not commonly used because 100% pure crystalline samples for most polymers are not available. One
alternative approach is to use the fusion enthalpy, the latent heat of melting,
351
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10.2 Differential Thermal Analysis and Differential Scanning Calorimetry
10 Thermal Analysis
of chemical repeated units (Hu ) to replace H100 in the calculations. Hu
can be calculated using the Flory relationship for the depression of the equilibrium melting temperature of a homopolymer due to the presence of low
molecular mass diluents. The Hu values of some polymers are available in the
literature.
A DSC curve can reveal the curing status of thermosetting polymers as illustrated
in Figure 10.16. During curing, polymer chains crosslink; this process releases
heat, which is reflected in the DSC curve. When a polymer is going through a
curing process, its DSC curve will show a broad peak at the curing temperature, as
shown in the curve of the first scan in Figure 10.16. When crosslinking is complete,
the curing peak disappears and is replaced by a feature of glass transition as shown
in the curve of the second scan in Figure 10.16.
DSC curves can also be used to identify individual polymers in a polymer
mixture. This is a rather unique capability of DSC or DTA. Figure 10.17 shows
DSC curves of plastic waste. The individual melting peaks reveal the waste’s
polymer content. By comparing these curves with DSC curves of pure polymers,
we can assign the melting peaks as those of low-density polyethylene (LDPE),
high-density polyethylene (HDPE), polypropylene (PP), Nylon-6, Nylon-66, and
polytetrafluoroethylene (PTFE).
A DSC curve can also reveal the thermal stability of polymers. For example,
a polyethylene sample is examined in isothermal conditions at 200 ◦ C with an
isothermal DSC curve versus time (Figure 10.18). The time when polyethylene
oxidation and degradation occurs is revealed by deviation of the DSC curve in
Figure 10.18. Comparing the times of oxidation for polyethylene with and without
using a stabilizer during processing, we know that the stabilizer has significantly
increased polyethylene’s resistance to oxidation at elevated temperatures.
Exo
DSC response
First scan
Second scan
Tg
T
Figure 10.16 Examining the curing status of epoxy resins. The first scan reveals the curing
process and the second scan shows a completion of curing. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. © 2001 Springer Science.)
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352
Endo
DSC response
PP
HDPE
LDPE
PTFE
Nylon-6
100
Nylon-66
200
T (°C)
300
Figure 10.17 DSC curves of plastic waste containing several polymers: low-density
polyethylene (LDPE), high-density polyethylene (HDPE), polypropylene (PP), Nylon-6™,
Nylon-66™, and polytetrafluoroethylene (PTFE). (Reproduced with kind permission of
Springer Science and Business Media from Ref. [1]. © 2001 Springer Science.)
Exo
DSC response
T = 200 °C
Polythene
+ stabilizers
Time
Figure 10.18 Isothermal DSC curve of polyethylene demonstrating the effectiveness of stabilizer to improve resistance to oxidation. (Reproduced with kind permission of Springer
Science and Business Media from Ref. [1]. © 2001 Springer Science.)
10.3
Thermogravimetry
TG is a technique for measuring mass change of a sample with temperature. A
sample to be measured is placed in a furnace and its mass change is monitored by a
thermobalance. The main application of TG is to analyze material decomposition and
thermal stability through mass change as a function of temperature in scanning
mode or as a function of time in the isothermal mode. TG curves are plotted
as mass change expressed in percent versus temperature or time. Figure 10.19
illustrates a typical TG curve in which the mass change is plotted against increasing
temperature. Decomposition of a sample is represented by two characteristic
temperatures: T i and T f . T i is the lowest temperature when the onset of mass
change is detected and T f is the lowest temperature when the mass change is
completed.
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10.3 Thermogravimetry
10 Thermal Analysis
Mass change/%
0
Ti
−50
Tf
−100
Reaction interval
Temperature/K
Figure 10.19 Thermogravimetric curves that exhibit decomposition starting temperature T i
and finish temperature T f . (Reproduced with permission from Ref. [3]. © 1999 John Wiley &
Sons Ltd.)
10.3.1
Instrumentation
The TG thermobalance structure is illustrated in Figure 10.20: it includes a microbalance, furnace, temperature programmer, and computer. The key component
is the microbalance, which measures the mass change. A typical microbalance
is able to measure mass change of ±1 μg with maximum mass of 100 mg. A
commonly used microbalance is the null-point type. The null-point microbalance
can maintain the sample in a vertical position when its mass changes. Figure 10.21
shows the structure of the commonly used null-point type microbalance, the Cahn
microbalance.
The Cahn microbalance senses the vertical displacement of a sample due to
mass change using an optical system. The optical system includes a light source,
a flag, a light tube, and a photodiode. The flag beneath the balance arm interferes
Microbalance
Computer
or
chart recorder
Furnace
Temperature
programmer
Sample and crucible
Figure 10.20 Structure of instrumentation. (Reproduced with permission from Ref. [3]. ©
1999 John Wiley & Sons Ltd.)
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354
Controls circuits
indicators
Rotational axis
of beam and coil
Coil
Balance beam
Hangdown
ribbon
Magnet
Light source
Hook
Taut band
ribbon
suspension
Tare
Flag
Light
tubes
Photodiode
Sample
Figure 10.21 Structure of a Cahn microbalance with capability to measure the mass loss
of a sample without the sample moving downward. (Reproduced with permission from
Ref. [2]. © 1993 Taylor & Francis Group Ltd.)
with light propagating from the source to the light detector (photodiode) when the
mass change is sensed by the balance beam. A feedback control system adjusts the
current in a magnetic-coil system and maintains the balance beam in its original
horizontal position even if the sample mass keeps changing.
The most common arrangement in TG instruments is when the sample is
connected to the microbalance by a suspension wire. The sample is located in the
center of a furnace, as illustrated in Figure 10.22. The furnace is designed as a
cylindrical tube with heating elements on its wall. The diameter of the tube is such
that it can accommodate a sample with relatively little open space. A thermocouple
is located in the tube axis and under the sample holder with a small gap in
between. Such a design can largely eliminate any temperature gradient among the
sample, thermocouple, and heating elements; it enables them all to reach thermal
equilibrium quickly. During operation, a protective gas will flow into and out of the
furnace tube to maintain an inert atmosphere during heating.
10.3.2
Experimental Aspects
10.3.2.1 Samples
Sample mass, volume, and form are important for recording accurate and reproducible TG curves. Reliable TG curves rely on minimization of deviation between
sample temperature and programmed temperature. Deviation typically results
from either endothermic or exothermic reactions in the sample and subsequent
heat transfer between heat source and sample. Sample mass is the most important
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10.3 Thermogravimetry
10 Thermal Analysis
Gas flow
Heat radiation
from furnace
windings
Thermocouple
Figure 10.22 Sample position in furnace in a TG system with protective gas flow downward. (Reproduced with permission from Ref. [2]. © 1993 Taylor & Francis Group Ltd.)
parameter affecting TG curves. In general, small sample mass is better than large
mass for minimizing temperature deviation. TG sample mass is usually about
several milligrams. The low limit of sample mass depends on the resolution limit
of the microbalance.
Samples can be in block, flake, fiber, or powder form. Sample form is the
second most important parameter affecting TG curves. The sample-form effect
on a TG curve is demonstrated in Figure 10.23, which shows the TG curves
of different forms of polymethyl methacrylate (PMMA). Decomposition of the
powdered PMMA sample occurs at lower temperature than it does with other
forms, as shown in the TG curves. A block sample should be ground or sliced to
obtain a suitable form for TG examination. We should avoid excessive force during
such mechanical processing, because mechanical deformation of the sample may
also affect the TG curves.
10.3.2.2 Atmosphere
TA can be run in either a reactive or nonreactive atmosphere. Reactive atmospheres
include corrosive, oxidizing, and reducing gases. Nonreactive atmospheres should
be an inert gas with little water vapor. Dry Ar and N2 are commonly used for
nonreactive atmospheres. Gas flows through the furnace tube around the sample
and carries volatile products out. A flow rate of 15–25 ml min−1 is recommended
for a sample mass of about 2–10 mg.
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356
Block
Mass change/%
−20
Powder
−40
Flake
−60
−80
−100
520
570
620
Temperature/K
670
720
Figure 10.23 Effects of sample form on TG curve of a polymethyl methacrylate (PMMA)
sample. Experimental conditions: 5 mg PMMA and a heating rate of 5 K min−1 . (Reproduced
with permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
Gas flow, however, generates concerns about possible thermal shielding and/or
buoyancy effects. Thermal shielding can be understood from Figure 10.22. Gas
flow downward to the sample holder will make the holder shield the thermocouple
junction from convective heat transfer through the flowing gas. Consequently, the
thermocouple junction temperature will not be the same as for a sample with
flowing gas. The buoyancy effect is illustrated in Figure 10.24. Gas flow upward will
Force
Figure 10.24 Buoyancy effects of upward protective gas flow. (Reproduced with permission
from Ref. [2]. © 1993 Taylor & Francis Group Ltd.)
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10.3 Thermogravimetry
10 Thermal Analysis
generate a lifting force on the sample holder. This effect is similar to weight loss
of a sample body in liquid. Such gas-flow effects are difficult to eliminate. Careful
calibration and good instrument design reduce such problems to a minimum.
10.3.2.3 Temperature Calibration
Temperature calibration is more complicated in TG instruments than in other
types of TA instruments because the thermocouple junction cannot touch either
the sample or sample holder. Good TA results can only be ensured with careful
temperature calibration. A Curie point method has been used to calibrate the
temperature of TG instruments. The Curie point is the transition temperature of
ferromagnetic materials where they lose ferromagnetism. Figure 10.25 illustrates
the Curie point method. A magnet is placed below the furnace. The total weight,
as measured by the microbalance, is the sum of sample weight plus the magnetic
downward force below the Curie point. When the Curie point of a ferromagnetic
sample is reached, the magnetic downward force disappears and weight loss will
be recorded in the TA curve, as illustrated in Figure 10.25b. The TG temperature
Mass
Furnace
Curie
point
Thermocouples
N
(a)
S
T
Magnet
(b)
Alumel 163 °C
Mass
Nickel 354 °C
Perkalloy 596 °C
Iron 780 °C
Hisat 50 1000 °C
200
(c)
400
600
T (°C)
800
1000
Figure 10.25 (a–c) The Curie point method for temperature calibration. (Reproduced with
kind permission of Springer Science and Business Media from Ref. [1]. © 2001 Springer
Science.)
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358
can be calibrated with several ferromagnetic materials with the Curie point in the
range 163–1000 ◦ C, as shown in Figure 10.25c.
The fusible line method can also be used as a calibration temperature. A fusible
wire with known melting temperature connects the microbalance suspension wire
and inert mass pieces. The fusible wire should locate the position of the sample in
the furnace. Melting of the wire at its melting temperature causes mass loss, which
is recorded in the TG curve.
10.3.2.4 Heating Rate
The heating rate affects TG curves considerably, similar to DTA and DSC. For
example, with endothermic decomposition, a high heating rate will increase the
starting and finishing temperatures of decomposition. Also, the temperature range
from start to finish will be wider at a higher heating rate than a lower heating
rate. Figure 10.26 shows an example of the effect of heating rate on the TG curve
of polyvinyl chloride (PVC). There are two reasons for heating-rate effects. First, a
high heating rate is more likely to generate a temperature difference between the
sample and thermocouple junction. The real sample temperature may lag behind
that of the thermocouple. Secondly, in decomposition with volatile products, it
takes time for those products to diffuse out of the sample and to be carried away by
flowing gas. A low heating rate is more likely to generate thermal equilibrium and
give a reproducible result for the analysis. A heating rate of about 5–10 ◦ C min−1 is
recommended for TG examination. For high-resolution TG examination, the rate
can be reduced to 1 ◦ C min−1 .
We can also use stepwise heating and dynamic heating instead of linear heating
in TG. Stepwise heating increases the temperature in small increments and then
maintains the temperature for a certain period. This heating manner may generate
a quasi-isothermal condition that provides sufficient time for thermal equilibrium
0
Mass change/%
−20
20 K/min
−40
−60
2 K/min
−80
−100
420
600
780
Temperature/K
Figure 10.26 Effects of heating rates on TG curves of powdered polyvinyl chloride (PVC).
Experimental conditions: 5 mg in dry N2 gas with a flow rate of 20 ml min−1 . (Reproduced
with permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
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10.3 Thermogravimetry
10 Thermal Analysis
and diffusion. Dynamic heating is flexible heating. The heating rate changes
smoothly and continuously in response to the rates of sample decompositions. For
example, the heating rate is fast in the temperature regions without thermal events,
but the rate is slow in the temperature regions where sample decompositions
occur.
10.3.3
Interpretation of Thermogravimetric Curves
10.3.3.1 Types of Curves
TG curves can be classified into seven types as illustrated in Figure 10.27. Type
(i) is a nearly horizontal line that indicates there is no decomposition with mass
loss of volatile products over the temperature range. Use of other types of TA
techniques may be necessary to find out whether a thermal event has occurred in
the temperature range. Type (ii) indicates a rapid mass loss at the initial stage of a
TA curve. It is likely that the sample has gone through drying or desorption. Type
(iii) is a one-stage decomposition curve that is typical in TG curves. It can define
(i)
(ii)
Mass
(iii)
(iv)
(v)
(vi)
(vii)
Temperature
Figure 10.27 Classification of thermogravimetric curves into seven types, each described in
the text. (Reproduced with kind permission of Springer Science and Business Media from
Ref. [1]. © 2001 Springer Science.)
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360
the stability limit of a sample. Type (iv) is a curve of multistage decomposition with
stable intermediates. Type (v) is also a curve of multistage decomposition, but there
is no stable intermediate. Type (v) may be a high heating-rate version of type (iv).
Rerunning a TG analysis of a sample showing a type (v) curve with a low heating
rate is necessary. Type (vi) indicates that a chemical reaction with mass gain has
occurred in the sample. A typical example is oxidation of metal samples. Type (vii)
indicates a mass-gain reaction occurs and then a mass-loss reaction occurs at a
higher temperature in the sample, which is rarely seen.
A slope change of a TG curve is the main feature used to analyze a sample.
Sometimes, the slope change is uncertain; in this case, a derivative thermogravimetry
(DTG) curve can be used. The DTG curve is a plot of dm
versus temperature.
dT
Figure 10.28 shows comparison of TG and corresponding DTG curves. A peak in a
DTG curve represents a maximum of mass change rate. DTG does not contain any
new information other than the original TG curve; however, it clearly identifies the
temperature at which mass loss is at a maximum.
Mass
Mass
TG
T
T
(a)
(b)
dm/dt
dm/dt
DTG
T
(a)
T
(b)
Figure 10.28 Schematic comparison of (a) TG curves and (b) corresponding DTG curves.
(Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. ©
2001 Springer Science.)
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10.3 Thermogravimetry
10 Thermal Analysis
ML = [(mS - mB)/mS] × 100
A
Mass change/mg
mS
C
mB
B
TA
TB
TC
Temperature/K
Figure 10.29 Temperature determination from a single-stage TG curve. (Reproduced with
permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
10.3.3.2 Temperature Determination
The determination of characteristic temperatures in TG curves is similar to that
in DTA and DSC curves. As illustrated in Figure 10.29, the temperature at which
decomposition starts is defined as the intersection of initial line tangent and
tangent of line portion when the slope changed. The finishing temperature of
decomposition is defined in a similar manner, as shown in Figure 10.29. A
midpoint temperature between the starting and finishing temperature can be
defined as T B , as shown in Figure 10.29.
10.3.4
Applications
The TG technique is simple but effective for assessing thermal stability and
chemical reactions by monitoring mass change in materials. Several reactions
involve mass change, including dehydration, desorption, decomposition, and oxidation. Figure 10.30 shows an example of TG analysis of the thermal stability of
CuSO4 ·5H2 O. Crystal water loss occurs at separated temperatures. Correspondingly, the structure of a sample goes through several stages of change during crystal
water loss. The thermal stability of polymeric materials is often a concern. The
way in which TG characterizes thermal stability of polymers is like a ‘‘fingerprint’’
method. Other characterization methods are often required to help us determine
the exact nature of reactions revealed by a TG curve.
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362
CuSO4.5H2O
Mass
CuSO4.3H2O
CuSO4.H2O
CuSO4
0
100
200
300
400
500
T(°C)
TG
NR
BR
DTG
dm/dt
Mass change/(arbitrary units)
Figure 10.30 TG curves of CuSO4 ·5H2 O in a range of ambient temperature to 500 ◦ C. (Reproduced with kind permission of Springer Science and Business Media from Ref. [1]. ©
2001 Springer Science.)
Oil/Plasticizer
500
600
700
800
Temperature/K
Figure 10.31 TG and DTG curves of a natural rubber–butadiene rubber blend. (Reproduced with permission from Ref. [3]. © 1999 John Wiley & Sons Ltd.)
TG curves do not always show obvious decomposition temperatures like
Figure 10.30. It is often desirable to plot DTG curves with TG curves to reveal the decomposition temperatures of polymers. Figure 10.31 shows an example
of polymer blend decomposition. Although TG curves revealed the decomposition
of the polymer blend of a natural rubber and a butadiene rubber, only the DTG
curves could clearly indicate the decomposition temperature of natural rubber, as
well as the higher decomposition temperature of butadiene rubber.
TG curves can also be used for quantifying compositions of composites containing thermally decomposable components. Figure 10.32 shows an example of using
the TG curves to determine the weight fraction of ceramic content in a polymer
matrix. It is quite often that the real content of particulates in a composite is not the
363
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10.3 Thermogravimetry
10 Thermal Analysis
100
Weight (%)
80
60
HA0/UHMWPE
HA10/UHMWPE
HA20/UHMWPE
HA30/UHMWPE
HA40/UHMWPE
HA50/UHMWPE
40
20
0
100
200
300
400
500
600
Temperature (°C)
Figure 10.32 TG curves of hydroxyapatite (HA)–ultrahigh molecular weight polyethylene
(UHMWPE) composites with different content HA particles. The legends indicate the nominal volume fraction of HA in the UHMWPE matrix.
same as the nominal content. Figure 10.32 demonstrates that the amount of ceramics (hydroxyapatite) in composites can be accurately determined by measuring the
weight differences in composite samples before and after the polymer (ultrahigh
molecular weight polyethylene) matrix is completely decomposed during heating
in TG analysis.
Questions
10.1 What are thermal events of materials?
10.2 List similarities and differences of DTA and DSC.
10.3 What thermal events of a semicrystalline polymer sample will be detected
by DSC? List them from low to high temperature.
10.4 Why should sample mass should be at the microgram level?
10.5 Why is a powder sample favorable in TA?
10.6 Sketch a DSC curve that shows a melting peak with a low and a high
heating rate.
10.7 What materials property does the slope change of a DSC curve indicate?
10.8 Why does a melting temperature not correspond to a peak temperature in
a DTA curve?
10.9 Determine PET melting temperature and crystallization temperature for
different heating and cooling rates from Figure 10.10.
10.10 People often run a sample twice in DSC or DTA. First, the sample is heated
and cooled at a constant rate, then the sample is heated again to obtain the
DSC curve for analysis. What are the reasons for this?
10.11 Show Eq. 10.11 is correct.
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364
10.12
10.13
10.14
10.15
Does TG always measure mass loss of sample? Why?
Does the Cahn microbalance balance mass change of a sample using a
counter weight? Why?
Sketch DTG curves in Figure 10.26.
How can TA be used to detect inorganic impurities in a polymer sample?
How can it be used to detect organic impurities in a polymer sample?
References
Further Reading
1. Brown, M. (2001) Introduction to Thermal
Hemminger, W. and Höhne, G. (1984)
Calorimetry–Fundamentals and Practice,
Verlag Chemie, Weinheim.
Haines, P.J. (2002) Principles and Thermal
Analysis and Calorimetry, Royal Society of
Chemistry, Cambridge.
Wunderlich, B. (2005) Thermal Analysis of
Polymeric Materials, Springer, Berlin.
Groenewoud, W.M. (2001) Characterization of
Polymers by Thermal Analysis, Elsevier, Amsterdam.
Scheirs, J. (2000) Compositional and Failure
Analysis of Polymers, John Wiley & Sons,
Inc., New York.
Analysis, Kluwer Academic Publishers,
Dordrecht.
2. Speyer, R.F. (1993) Thermal Analysis of Materials, Marcel Dekker,
New York.
3. Hatakeyama, T. and Quinn, F.X.
(1999) Thermal Analysis: Fundamentals
and Applications to Polymer Science,
2nd edn, John Wiley & Sons, Ltd,
Chichester.
4. Charsley, E.L. and Warrington, S.B.
(1992) Thermal Analysis: Techniques and
Applications, Royal Society of Chemistry,
Cambridge.
365
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Further Reading
Index
a
aberrations 7–9
abrasive cutting 16
absorbance 303
absorption contrast 96
absorption edge 50–51
acceleration voltage and probe current
144–145
achromatic lens 14
adatom 168–169
adhesive clamping 18
analyzer 33, 36
angular position of detector. See take-off
angle
angular quantum number 193
anti-Stokes scattering 289
aperture diaphragm 11–12
aperture size 141–143
apochromatic lens 14
astigmatism 8, 145
asymmetric stretching mode
290, 294
atomic force microscope (AFM) 163, 165,
180–182
– dynamic noncontact mode applications
181–183
– force modulation applications 182
– force sensors 172–174
– near-field forces 170–172
– operational modes 174–180
– static mode applications 180–181
– tapping mode applications 182
atomic number factor 216
atomic scattering factor 60
Auger electron 192, 194
Auger electron spectroscopy (AES)
221–225, 233–235, 239–241, 241, 243–244,
246–247
b
background noise 133–134
background spectrum 302
backscatter coefficient 139–140
backscattered electrons (BSEs) 129–130,
135, 137, 139–140, 216
barrier filter 38
baseline method, for absorbance
determination 329
beam brightness 131
Beer’s Law 329–330
bending contours 120–122
bending modes 290–291
birefringence 31
body-centered cubic (BCC) structure 111
borax fusion 207
Bragg angle 68, 69, 76
Bragg’s law 52–53, 69, 76, 96, 107, 118–119,
199–201, 313, 314
Bragg-Brentano arrangement 63–64
bright-field imaging 98–100
bright-field imaging 26–28
brightness 5
c
Cahn microbalance 354–355
calibration 239
camera constant 107
camera length 107
cantilever force 176
capillary forces 172
Cassegrain lens 307
cationization 271
characteristic X-rays 48–51, 191–193, 204
– comparisons 194–196
– selection rules 193–194
charge neutralization 241
charged-coupled device (CCD) 153, 314
Materials Characterization: Introduction to Microscopic and Spectroscopic Methods, Second Edition. Yang Leng.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
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367
Index
chemical shift 235, 239–241
chromatic aberration 7
cold crystallization 341
cold field emission gun 86–87
cold mounting 18–19
collector lens 10
collision cascade 254, 257
collision sputtering 254
color temperature 9
colored filters 13
composition determination, with Raman
spectroscopy 319–321
compositional contrast 139–141
compositional depth profiling 247–249
concentric hemispherical analyzer (CHA)
229–230, 233
condenser annulus 29
condenser lens 10, 39, 128
conductive film coating 148
confocal diaphragms 312
confocal laser scan microscopy (CLSM) 39
– three-dimensional images 41–43
– working principles 1–40
conjugate aperture planes 11
conjugate field planes 11
conjugate focal planes 11
constant analyzer energy (CAE) 229
constant retarding ratio (CRR) 229–230,
233
constant-current mode 168
constant-height mode 168
contact and noncontact modes 174–175
continuous X-rays 48
contrast 6, 94–95
– formation 135
– – compositional contrast 139–141
– – electron- specimen interactions 135–137
– – topographic contrast 137–139
– phase contrast 15, 26–27, 29–31, 101,
103–106, 125
– – theoretical aspects 102
– – two- beam and multiple–beam imaging
105
convergence angle of probe 131
creep deformation 186
critical angle 206
critical-point drying 149–150
crossed position 33, 36
crystal defect images 117
– bending contours 120–122
– dislocations 122–124
– wedge fringe 117–120
crystallographic contrast 141
crystallographic orientation determination
with Raman spectroscopy, 322–323
Curie point 358–359
curvature of field 8–9
d
d-spacing 71, 76–77, 113, 200
damaged surface area 255
dark-field imaging 26–28, 98–101
dead time, of detector 205
Debye rings 58
degenerate vibrations 290
dehydration 149–151
density of state 167
depth of field 6–7, 141–143
depth of focus 7
depth resolution 277
derivative thermogravimetry 361
detection limit 277
detection sensitivity 277
deuterated triglycine sulfate (DTGS) 301
deviation vector 119
diamond saw 16
diatomic model, of molecular vibration 285,
290
dichroic mirror 37–38
differential interference contrast (DIC) 15,
35–36
differential mode spectrum 233
differential scanning calorimetry (DSC) See
also differential thermal analysis (DTA)
337–340
– application to polymers 351–353
– enthalpy change measurement 347
– heat capacity determination 348–350
– temperature-modulated differential
scanning calorimetry (TMDSC)
340–342
differential thermal analysis (DTA) See also
differential scanning calorimetry (DSC)
337, 339–340, 348
– baseline determination 343–344
– calibration of temperature and enthalpy
change 348
– phase transformation and phase diagrams
350–351
– sample requirements 342–343
– scanning rate effects 344–345
– transition temperatures 345–347
– working principles 337–338
diffraction contrast 96–101
diffraction grating 311, 313–314
dipole moment of molecule 293
diffuse reflectance 305–306
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368
direct collision sputtering 254
direct comparison method 74–75
direct imaging method 315
direct mode spectrum 233
dislocations 122–124
double refraction. See birefringence
double transmission 306
double-tilt holder 89–90
duoplasmatron source 259–260
dynamic mode 174–175
– noncontact mode 177–178
– – applications 181–183
dynamic range 277
dynamic secondary ion mass spectrometry
253, 257
e
elastic scattering 130, 287–288
electric discharge machine (EDM) 16
electrolytic polishing 22–23
electrolytic thinning 91–92
electromagnetic lenses 87–89, 128
electromagnetic radiation 283–284
electron backscatter diffraction (EBSD) 151
– applications 155–156
– indexing and automation 153–155
– pattern formation 151–153
electron bombardment sources 259–260
electron channeling contrast. See
crystallographic contrast
electron energy analyzers 229–230
electron energy resolution 229
electron flood gun 241, 266
electron gun 228–229
electronic gate 260
electron number effect 138–139
electron retardation 216, 229
electron sources 84–85, 87
– field emission gun 86–87
– thermionic emission gun 85–86
electron spectroscopy 221
– Auger electron spectroscopy 222–225
– characteristics
– – Auger electron spectra 233–235
– – photoelectron spectra 230–233
– compositional depth profiling 247–249
– instrumentation 225
– – electron energy analyzers 229–230
– – electron gun 228–229
– – electronic gate 280
– – ion gun 229, 247
– – ultrahigh vacuum system 225–227
– – X-ray gun 227–228
– qualitative analysis 235, 237–239
–
–
–
–
–
–
– chemical shifts 239–241
– insulating material problems 241–245
– peak identification 239
quantitative analysis
– peaks and sensitivity factors 246–247
– X-ray photoelectron spectroscopy
221–222
electronic gate 280
electrostatic forces 171–172
elliptically polarized light 32
emission volume 210
endothermic thermal event 337, 339
energy dispersive spectroscopy (EDS) 127,
197, 203–208
– advances 204–206
– detector 203–204
– scanning modes 210–211
– special features 208–210
enthalpy change 334–335
environmental scanning electron microscope
(ESEM) 156
– applications 158–159
– working principle 156–158
epi–illumination 12, 37, 38
etchants 23–25
etching 23–26
Everhart–Thornley (E–T) detector 130
Ewald sphere 55–58, 96, 108
exciter filter 37
exothermic thermal event 337, 339
external standard method 74
eyepiece 1–3, 15
– dept of field improvement 15
– optimum resolution steps 15
f
face-centered cubic (FCC) structure 111, 119
far-field interactions 163
Faraday cage 130, 141
Fermi level 167
field diaphragm 11–12
field emission gun 86–87, 127, 131
final thinning 91
– electrolytic thinning 91–92
– ion milling 92–93
– ultramicrotomy 93–94
fingerprint region 324
first-order phase transition 334
flood gun 266–267
fluorescence factor 217
fluorescence microscopy 37–39
fluorescent labeling 37
fluorescent yield 195–197
fluorochromes 37
369
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Index
Index
force modulation 179–180
– applications 182
force sensors 172–174
Fourier transform (FT) 103–104, 275
Fourier Transform infrared spectroscopy
(FTIR) 297–298
– examination techniques
– – liquid and gas sample preparation
304–305
– – microspectroscopy 307–310
– – reflectance 305–306
– – solid sample preparation 304
– – transmittance 304
– instrumentation
– – beamsplitter 300–301
– – Fourier Transform infrared spectra
302–304
– – infrared detector 301
– – infrared light sources 300
– working principles 298–300
freeze drying 150–151
friction force microscopy. See lateral force
microscopy
fundamental parameter method 215
fusible line method 359
fusion enthalpy 351
g
gas–discharged tubes 10
gaseous detection devices (GDD)
Globar 300
goniometer circle 64
grinding 19–21, 91
group theory 292
158
i
illumination system 9–13
image artifacts 183
– scanner 185–187
– tip 184–185
– vibration and operation 187–188
image formation 1–3
imaging modes 26, 94–95
– bright–field and dark–field imaging
26–27
– diffraction contrast 96–101
– fluorescence microscopy 37–39
– mass-density contrast 95–97
– Nomarski microscopy 35–37
– phase contrast 101–106
– phase–contrast microscopy 27–30
– polarized–light microscopy 30–35
immersion etching 24
inelastic scattering 130
– See also Raman scattering 115, 311
infinity–corrected optics 2
infrared absorption 286–287
infrared activity 292–295
inphase 52
instrument baseline 343
interface smearing 248–249
interference filters 13
interferogram 298–300
intermittent contact mode. See tapping mode
internal standard method 74, 214–215, 330
interpretable structure image 105
ion gun 229, 247
ion milling 92–93
ionization probability 255–256, 278
h
k
Hamasker constant 171
hand grinding 19–20
hand polishing 21–22
harmonic vibrations 285
heat 335
heat filters 13
heat flux differential scanning calorimetry
338, 339
heat tinting 26
hemispherical sector analyzer 229
Hertz model 176
high-resolution transmission electron
microscopy (HRTEM) 101
high-resolution X-ray diffractometry
(HRXRD) 64–65
holographic filter 311, 312
hot mounting 17–18
Hough transform 154
Kα doublet 50
Köhler system 10–12
Kikuchi lines 114–117
Kikushi band 152–154
kinetic component, of heat flow
341
l
lanthanum hexaboride gun 85–86
laser scanning 40
laser source 311
lattice vibrations 286
lens aberrations 7
lifetime, of surface 257–258
light dispersion 7
light filters 12–13
light guide 130
light microscopy 1
– confocal laser scan microscopy (CLSM)
39
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370
–
–
–
–
– three–dimensional images 41–43
– working principles 39–40
imaging modes 26
– bright–field and dark–field imaging
26–27
– – fluorescence microscopy 37–39
– – Nomarski microscopy 35–37
– – phase–contrast microscopy 27–30
– – polarized–light microscopy 30–35
– instrumentation 9
– – eyepiece 15
– – illumination system 9–13
– – objective lens 13–15
– optical principles
– – aberrations 7–9
– – depth of field 6–7
– – image formation 1–3
– – resolution 3–6
– specimen preparation 15–16
– – etching 23–26
– – grinding 19–21
– – mounting 17–19
– – polishing 20–23
– – sectioning 16–17
linear absorption coefficient 50
liquid-metal ion sources 260–261
local density of states (LDOS) 167–168
m
machine grinding 20
magnetic contrast 141
magnetic quantum number 193
magnetic sector analyzer 263–264
magnification 3
manipulation mode 168–169
mass absorption coefficient 50–51
mass analysis system 262–263
– magnetic sector analyzer 263–264
– quadrupole mass analyzer 264, 267
– time-of-flight analyzer 264–265
mass density 50
mass resolution 263
mass-density contrast 95–97
mass-to-charge ratio 263
matrix factor 214
mechanical clamping 18
mercury cadmium telluride (MCT) 301, 307
metallography 1, 23
Michelson interferometer 298, 313–314
microanalysis 208
micro-Raman. See Raman microscopy
Miller indices 53, 61, 66, 111
Moseley’s Law 192
mounting 17–19
mull method 304
multicrystal diffraction 114
multiplet splitting 233
n
n-mer region 271
near-field forces 170–171
– capillary forces 172
– electrostatic forces 171–172
– short-range forces 171
– van der Waals forces 171
near-field interactions 163
Nernst glower 300
neutral density (ND) filters 13
Nomarski microscopy 35–37
normal mode, of molecular vibrations
289–291
– classification of normal vibration modes
291–292
– number of normal vibration modes 291
null-point microbalance 354
numerical aperture (NA) 3, 13–14
o
object 1
object functions 102–103
objective lens 1, 2, 13–15, 102–104, 128
oligo-scattering condition 157
oligomer region 271
Olympus light microscope 10
opening angle 184
operational modes 168–176
– dynamic operational modes 177–180
– lateral force microscopy 177, 181
– static contact modes 176–177
optical anisotropy 30, 34
p
parafocusing 64
parallel imaging method 245
pass energy 229
phase contrast 101–102
– theoretical aspects 102–105
– two-beam and multiple-beam imaging
105–106
phase identification, with Raman spectroscopy
317–318
phase imaging 179
phase plate 29
phase shift 104
phase–contrast microscopy 27–30
photoelectron spectra 230–233
photomultiplier tube 130
photon energy 284
371
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Index
Index
piezoelectric materials 165
pinhole aperture 39
pinhole spatial filter 311–312
plane–polarized light 31
plasma ion sources 259
plasma–magnetron sputtering 149
Plasmon loss 233
pleochroism 33
polarizability 295
polarizability ellipsoid 295–297
polarization factor 59
polarized–light microscopy 30–35
polarizer 31
polishing 20–23
polishing cloth 21
polymer identification, with Raman
spectroscopy 319
potassium bromide 300
powder diffraction file (PDF) 70–73
power-compensated differential scanning
calorimetry 339, 347
prefilters 312–313
pressure-limiting aperture (PLA) 156–157
primary absorption 214
primary beam
– analysis area 279–280
– energy 278
– incident angle 278–279
primary ions 258–259, 266
– sources 259–261
– Wien filter 262
principal quantum number 193
probe diameter 131
projector lens 1
q
quadrupole mass analyzer 264
quantitative differential thermal analysis
(DTA). See heat flux differential scanning
calorimetry
quantum numbers 193
r
Raman active 292
Raman activity 292–293, 295–297
Raman imaging 315–316
Raman microscopy 310
– applications 316–323
– fluorescence problem 314–315
– instrumentation 310–314
– Raman imaging 315–316
Raman scattering 287–288
Raman shift 289, 314, 327
Raman spectra quantitative analysis 330
raster 39
ratio method 329–330
reciprocal lattice 53–55
reflected–light microscopes 9, 23, 28, 30
reflection–absorption 305
relay lens 12
remote aperture 307
residual strain determination with Raman
spectroscopy 321–322
resolution 3–5
– brightness and contrast 5–6
– effective magnification 5
Rose viability criterion 134
rotation angle 112
s
sample baseline 343–344
scan coils 128
scanning Auger microscopy 225
scanning electron microscopy (SEM) 83,
127, 207–208, 225, 315
– contrast formation 135
– – compositional contrast 139–141
– – electron–specimen interactions
135–137
– – topographic contrast 137–139
– electron backscatter diffraction (EBSD)
151
– – applications 155–156
– – indexing and automation 153–155
– – pattern formation 151–153
– environmental scanning electron
microscope (ESEM)
– – applications 158–159
– – working principle 156–158
– instrumentation
– – optical arrangement 127–129
– – probe size and current 131–135
– – signal detection 129–131
– operational variables 141
– – acceleration voltage and probe current
144
– – astigmatism 145
– – working distance and aperture size
141–143
– specimen preparation 145–146
– – dehydration 149–151
– – microcomposition examination
preparation 149
– – topographic examination preparation
146–149
scanning force microscope (SFM). See atomic
force microscope (AFM)
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372
scanning method, for compositional imaging
244–245
scanning probe microscopy (SPM) 163
– atomic force microscopy (AFM)
– – dynamic noncontact mode applications
177–183
– – force modulation applications 182
– – force sensors 172
– – near-field forces 170–172
– – operational modes 174–180
– – static mode applications 180–181
– – tapping mode applications 182
– image artifacts 183
– – scanner 185–187
– – tip 184–185
– – vibration and operation 187–188
– instrumentation 163–164
– – control and vibration isolation 165–166
– – instrumentation 165
– scanning tunneling microscopy (STM)
– – applications 169–170
– – operational modes 168–169
– – probe tips and working environments
167–168
– – tunneling current 166–167
scanning tunneling microscopy (STM) 163,
165–166
– applications 169–170
– operational modes 168–169
– probe tips and working environments
167–168
– tunneling current 166–167
scattering vector magnitude 79
scintillator 130
second-order phase transition 334
secondary absorption 214
secondary electrons (SEs) 129–130, 135,
137, 139, 141
secondary fluorescence 214
secondary ion mass spectrometry (SIMS)
253
– basic principles 253–254
– – dynamic and static SIMS 257–258
– – generation 254–257
– depth profiling 275–276
– – generation 276–277
– – optimization 276–280
– imaging 272
– – generation 274
– – quality 275
– instrumentation 258
– – mass analysis system 262–265
– – primary ion system 258–262
– surface structure analysis 266
– – experimental aspects 266–268
– – spectrum interpretation 268–272
second-order phase transition 334
sectioning 16
– cutting 16–17
– microtomy 17
selected-area diffraction (SAD) 107
– characteristics 107–109
– Kikuchi lines 114–117
– multicrystal diffraction 114
– single-crystal diffraction 109–114
semiachromatic lens 14
sensitivity factor 246–247
shake-up satellites 231–233
short-range forces 171
Siegbahn Notation 194
signal detection and SEM 129–130
– detector 130–131
single-beam spectrum 302
single-crystal diffraction 109
– crystal phase identification 112–114
– cubic crystal pattern indexing 89–112
single-tilt holder 89
slow collision sputtering 276
small-angle X-ray scattering (SAXS) 79
Soller slits 62
specimen scanning 39–40
spectroscopic mode 168
specular reflectance 305–306
spherical aberration 7–8, 104
spin quantum number 193
sputtering 148–149
– collision sputtering 254
– direct collision sputtering 254
– plasma–magnetron sputtering 149
– slow collision sputtering 254
– thermal sputtering 254
sputter yield 247–248, 281
stage number 320
standardless quantitative analysis 217–218
static mode 174, 174–175
– applications 180–181
static secondary ion mass spectrometry 253,
257–258
Stokes scattering 289
stopping factor 216
structure extinction 60–61
structure factor 61
submonomer region 269, 271
surface ionization sources 261
surface structure analysis 266
– experimental aspects
– – flood gun 266–267
– – primary ions 266
373
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Index
Index
thermogravimetry (TG) 353–354
– applications 362–364
– atmosphere 356
– curve types 360–361
– heating rate 359
– instrumentation 354–355
– samples 355–356
– temperature calibration 358–359
t
– temperature determination 362
take-off angle 208
thin-film X-ray diffractometry 63
tapping mode 174–175, 177–179
time-of-flight analyzer 264–265
– applications 182
time-of-flight secondary ion mass
Taylor cone 261
spectrometry (TOF SIMS) 262,
thermal analysis (TA) 333
270–272
– common characteristics
tint etching 24, 26
– – experimental parameters 336–337
tip geometry 184–185
– – instrumentation 335–336
tip jump-off-contact 175
– – thermal events 333–335
tip jump-to-contact 175
– differential thermal analysis (DTA) and
topographic contrast 137–139
differential scanning calorimetry (DSC)
topographic examination preparation
337–340, 348
146–147
– – application to polymers 351–353
– surface charging and prevention
– – baseline determination 343–344
147–149
– – calibration of temperature and enthalpy
total reflection X-ray fluorescence
change 348
spectrometer (TRXRF) 205–206
– – enthalpy change measurement
trajectory effect 137–138
347
transfer function 104
– – heat capacity determination
transmission 255
348–350
transmission electron microscopy 83
– – phase transformation and phase diagrams – crystal defect images 117
350–351
– – bending contours 120–122
– – sample requirements 342–343
– – dislocations 122–124
– – scanning rate effects 344–345
– – wedge fringe 117–120
– – temperature-modulated differential
– image modes 94–95
scanning calorimetry (TMDSC)
– – diffraction contrast 96–101
340–342
– – mass-density contrast 95–97
– – transition temperatures 345–347
– – phase contrast 101–106
– – working principles 337–338
– instrumentation 83–84
– – thermogravimetry (TG) 353–354
– – electromagnetic lenses 87–89
– – applications 362–364
– – electron sources 84–87
– – atmosphere 356
– – specimen stage 89–90
– – curve types 356–358
– selected-area diffraction (SAD) 107
– – heating rate 359
– – characteristics 107–109
– – instrumentation 354–355
– – Kikuchi lines 114–117
– – samples 355–356
– – multicrystal diffraction 114
– – temperature calibration 358–359
– – single-crystal diffraction 109–114
– – temperature determination 361, 362
– specimen preparation 90
thermal drift 168, 186
– – final thinning 91–94
thermal events 333–334
– – prethinning 91
– enthalpy change 335
transmittance spectrum 303
thermal field emission gun 86
transmitted–light microscopes 9, 23
thermal sputtering 254
tungsten filament gun 85–86
thermionic emission gun 85–86
Tungsten–halogen bulbs 9–10
tunneling current 166–167
thermobalance 353
surface structure analysis (contd.)
– – sample handling 267–268
– spectrum interpretation 268–269
– – element identification 269–272
surface topography 167
swab etching 24
symmetric stretching mode 290
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374
u
ultrahigh molecular weight polyethylene
(UHMWPE) 79
ultrahigh vacuum system 225–227
ultramicrotomy 17, 93–94
v
vacuum evaporating 148
vacuum impregnation 18–19
van der Waals forces 171
vibrational quantum number 286
vibrational spectroscopy, for molecular
analysis 283
– electromagnetic radiation 283–284
– Fourier Transform infrared spectroscopy
(FTIR) 297–298
– – examination techniques 304–310
– – instrumentation 300–304
– – working principles 298–300
– infrared activity 292–295
– interpretation 323
– – band intensities 327
– – characteristic bands identification
324–327
– – infrared spectra quantitative analysis
327, 329–330
– – Raman spectra quantitative analysis
330
– – spectrum comparison 323
– molecular vibrations
– – normal mode 289–292
– – origins 285–286
– principles
– – infrared absorption 286–287
– – Raman scattering 287–288
– Raman activity 292–293, 295–297
– Raman microscopy 310
– – applications 316–323
– – fluorescence problem 314–315
– – instrumentation 310–314
– – Raman imaging 315–316
virtual image 1
w
wave function 103–104
wave number 284
wavelength dispersive spectroscopy (WDS)
199–204
– analyzing crystal 200–201
weak-beam dark-field image 101
wedge fringe 117–120
Wehnelt electrode 85
white X-rays. See continuous X-rays
wide-angle diffraction (WAXD)
75–79
wide-angle scattering (WAXS) 75, 79–81
Wien filter 262
Wollaston prisms. See differential
interference contrast (DIC)
working distance 131
– and aperture size 141–143
x
X-ray absorption factor 216–217
X-ray diffraction methods 47
– diffraction geometry
– – Bragg’s law 52–53
– – Ewald sphere 55–58
– – reciprocal lattice 53–55
– diffraction intensity 58–60
– – applications 70–75
– – diffraction data acquisition and treatment
65–67
– – diffraction spectra distortions 67–70
– – instrumentation 62–65
– – sample preparation 65
– – structure extinction 60–61
– wide-angle diffraction (WAXD) 75–79
– wide-angle scattering (WAXS) 75, 79–81
– X-ray diffractometry (XRD) 62
– X-ray radiation
– – absorption 50–51
– – generation 47–50
X-ray diffractometer 62, 65, 68, 196
X-ray diffractometry (XRD) 62, 108, 211, 213
– applications
– – crystal-phase identification 70–72
– – quantitative measurement 72–75
– diffraction data acquisition and treatment
65–67
– diffraction spectra distortions
– – crystallite size 68–69
– – preferential orientation 67–68
– – residual stress 69–70
– instrumentation 62–63
– – system aberrations 64–65
– sample preparation 65
X-ray fluorescence (XRF) 191, 196, 199,
211–215
– energy dispersive spectroscopy (EDS) 203
– – advances 204–206
– – detector 203–204
– wavelength dispersive spectroscopy (WDS)
199–203
– working atmosphere and sample
preparation 206–207
X-ray gun 227–228
375
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Index
Index
X-ray photoelectron spectroscopy (XPS)
221–222, 227, 229–231, 235, 237–241,
243–245, 247–248, 250
X-ray photons 203–205, 210
X-ray scattering 59–60
X-ray spectroscopy 191
– characteristic X-rays 191–193
– – comparisons 194–196
– – selection rules 193–194
– energy dispersive spectroscopy (EDS) in
electron microscopes 207–208
– – scanning modes 210–211
– – special features 208–210
– fluorescence spectrometry (XRF)
196, 199
– – energy dispersive spectroscopy
203–206
– – wavelength dispersive spectroscopy
(WDS) 199–203
– – working atmosphere and sample
preparation 206–207
– qualitative analysis 211–213
– quantitative analysis 213–214
– – electron microscopy 216–218
– – fundamental parameter method
215
– – X-ray fluorescence 214–215
X-ray tube 48
z
ZAF method 216–217
zero line. See instrument baseline
zero path difference 298
zone axis direction 55
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376